A circle having a radius of ? =1/2(3 + 2√2) ?? is cut into segments by a chord which is √2 ?? from the center of the circle. Compute the following: a) the area of the smaller segment and b) the perimeter of the segment.

A circle having a radius of ? =1/2(3 + 2√2) ?? is cut into segments by a chord which is √2 ?? from the center of the circle. Compute the following: a) the area of the smaller segment and b) the perimeter of the segment.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.5: More Area Relationships In The Circle

Problem 5E: In the circle, the radius length is 10 in. and the length of AB is 14 in. What is the perimeter of...

See similar textbooks

Related questions

Q: Draw and solve. A concrete octagonal pier of height 15 ft. is to be resurfaced. If each of the base…

A: Given that: A concrete octagonal pier of height 15 ft and base edge = 1.5 ft

Q: Given the triangle shown with base b and height h: Assume that b + h = 25; what formula will…

A: Given, base = b Height = h b +h =25 We have to find the area of triangle that will maximize the…

Q: In the Figure, CB is a diameter of a circle with a radius of 2 cm and center O, A ABC is a right…

A: Figure : CB is the diameter; OB= 2 cm…

Q: This figure is formed by a square and an isosceles trapezoid. 4 In. 5 in. 10 in. What is the…

A: To find the perimeter

Q: What is a simplified formula for the area of an equilateral triangle in terms of length of a side…

A: To determine a simplified formula for the area of an equilateral triangle in terms of length of a…

Q: - equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting…

A: let the length of the lots =L and breadth of the lots= x area of the lots = L×x It is given that…

Q: The perimeters of two regular hexagons are 30 in. and 72 in. What is the ratio of their apothens? Of…

Q: In circle D, AB is a diameter. A 23. If mZADC=3x+10 and mBC = 2x- 30, what is m AC?

Q: Given a trapezoid with an area of 90 ft² and bases of 15 and 21 ft, find the length of the height.

Q: The length of the base is and the length of the height is Therefore the area of the triangle is x x…

A: formula:

Q: The area of a regular hexagon is 144 m^2. What is the new area of the regular hexagon if the apothem…

Q: A circle has a diameter of 28 - A trapezoid has bases x and (x+2) and a height of 4.

Q: Two regular octagons have perimeters 16 cm and32 cm, respectively. What is the ratio of their areas?

A: Given the perimeters of the reegular octagons are 16 cm and 32 cm. Thus for the first regular…

Q: 5. Given: In circle 0, OA = 5, BC = 6, and CD = 4 Find: Area of Quadrilateral ABCD

A: (5). Given: OA=5BC=6CD=4

Q: Given the area of the trapezoid (2000 m^2) and the side of one base (144 m), find the length of the…

A: Given. Area of Trapezoid ABCD, A=2000m2 one base length AB=144…

Q: Given the edge of a square is about 100 cm, by how to measure it such that the

Q: A side of an equilateral triangle is 26 yd long. What is the area of the triangle? Do not round any…

Q: The area of a trapezoid is 42 in^2. What is the new area of the trapezoid if the height were tripled…

Q: In a regular polygon with each side of length 6.5 cm, the perimeter is 130 cm. How many sides does…

A: A regular polynomial is a polynomial in which all the angles are equal and also all the sides are…

Q: 2. What is the perimeter needed to fence a right triangle with legs 63ft and 16 ft? from

A: The objective of the question is evaluate the perimeter of the right triangle.

Q: 0, Find a formula for the area of the triangle whose vertices are in R?. V1, and V2

Q: 2.) Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long.…

A: We can find the area as below.

Q: The area of a right triangle whose sides have lengths 5 in., 12 in., and 13 in. is exactly 30 in?.…

A: The area of right triangles having sides 5 in., 12 in. and 13 in. is exactly 30in2. To Evaluate The…

Q: For a crane to lift the beam shown to the right, the beam and the two support cables must form an…

A: Given that the distance between the cables along the beam is 18 ft and the height h is 8 ft. The…

Q: The length of the radius of the inscribed circle of a regular n-gon is called the apothem of the…

A: Let A denote the area of a regular n-gon and P be the perimeter of a regular n-gon. The regular…

Q: A 20 feet wire is cut into two pieces. To form an isosceles triangle and a circle, find the…

A: Given: The length of the wire is 20 ft. The wire is cut into two pieces. Let the length of the first…

Q: For a regular octagon, the length of the apo- them is approximately 12 cm and the length of the…

Q: If the area of a trapezoid is 929 units2, and the lengths of the two bases are 17 & 28, what is the…

Q: In the accompanying diagram, AABC is not isosceles. Prove that if altitude BD were drawn, it would…

Q: An architect designed a semicircular tunnel so that two trucks can pass each other with a 3-foot…

A: Let radius of semicircular tunnel be r, then its diameter will be 2r. Given: Height of truck=12…

Q: Find the length of the radius in a regular decagon for which each apothem has a length of 12.5 cm.

A: Given that, the length of apothem in a regular decagon is 12.5 cm. Now, since the regular decagon…

Q: E. Prove that if semicircles are constructed on each of the sides of a right triangle, then the area…

A: In triangle ABC, using pythagorus theorem - c2 = a2+b2 .............(1)Semicircle on…

Q: Given: AABC, whose sides are 13 in., 14 in., and 15 in. Find: a) BD, the length of the altitude to…

A: Given: △ABC, whose sides are 13 in., 14 in., and 15 in. a) Given BD is the altitude to the base of…

Q: A rectangle is the polygon whose formula for area is most similar to that of a parallelogram. O True…

A: Topic:- parallelogram and rectangle

Q: A picture frame is in the shape of a square with a circle removed from the centre. If the radius of…

A: Given, a picture frame is in the shape of a square with a circle removed from the centre. if the…

Q: From a circular piece of metal sheet with diameter 20 cm, a rectangular piece with perimeter 28 cm…

A: Approach : The diagonal of rectangle becomes equal to the diameter of the circle.

Q: The area of a triangle inscribed in a circle having a radius 9cm9cm is equal to…

A: We have to find other side of the triangle.

Q: The perimeter of OSTOP is 54 cm, and ST is I cm longer than SP. Find ST and SP.

A: The Perimeter of a Parallelogram STOP is 54 cm. ST is 1 cm longer than SP. To find: ST and SP

Q: If a has a length of x units and c has a length of 2x units, what will be the length of b?

Q: The perimeters of two regular hexagons are 30 in. and 72 in. What is the ratio of their apothems? Of…

Q: The area of the circle circumscribing about an equilateral triangle is 254.47 sq m. What is the area…

Q: If a triangle has sides of length x, x+2, and x-4, what is the perimeter of the triangle in terms of…

A: Given information- We have given the length of sides of a triangle x, x+2, x-4 We have to find the…

Q: A hexagon is inscribed in a circle. If the difference between the area of the circle and the area of…

A: The side of the hexagon and the radius of the circle will be the same, consider a. The difference in…

Q: Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm,…

Q: The outer circle of the driveway has a diameter of 30 feet and the inner circle of the driveway has…

A: Area of circle

Q: The apothem of a regular hexagon is 5/3 in. What is the length of its sides? What is its area?…

Q: For a rectangle with area 225 to have the smallest perimeter, what dimensions should it have? (Enter…

A: For the minimum perimeter of the rectangle you just need to equate the derivative of perimeter…

Q: For a regular pentagon, the length of the apothem is 12 in. Find the length of the pentagon's radius…

A: Given: Apothem of a regular pentagon is, a=12 inches. The objective is to find the length of the…

Q: In a circle whose radius is 10cm, a chord is 6cm from the center. How long is the chord?

Q: Consider a right triangle whose hypotenuse has a length of 53 in. If one leg is 17 in longer than…

A: Given: Length of 53 in One leg is 17 in

Question

A circle having a radius of ? =1/2(3 + 2√2) ?? is cut into segments by a chord which is √2 ?? from the center of the circle. Compute the following:

a) the area of the smaller
segment and

b) the perimeter of the segment.

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

For a right circular cone, the slant height has a measure equal to twice that of the radius length of the base. If the total area of the cone is 48in2, what are the dimensions of the cone?
In the circle, the radius length is 10 in. and the length of AB is 14 in. What is the perimeter of the shaded sector?
A baseball diamond is really a square with sides of 90 feet. How far is it from home plate to second base, as shown?
The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Given regular octagon RSTUVWXY with each side of length 4, find the length of diagonal RU. HINT: Extended sides, as shown, form a square.
The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Circle O has a diameter of length 20cm. Chord AB has length 12cm, and chord CD has length 10cm. How much closer is AB than CD to point O?
Each side of square RSTV has length 8. Point W lies on VR- and point Y lies on TS- in such a way to form parallelogram VWSY, which has an area of 16units2. Find the length of VW-.
For a regular octagon, the length of the apothem is approximately 12 cm and the length of the radius is approximately 13 cm. To the nearest centimeter, find the perimeter of the regular octagon.