b) Show more generally that the lines joining any point on a circle to the endpoints of a given diameter and to the endpoints of a given chord perpendicular to the diameter form a harmonic pencil.

Q: To test for symmetry with respect to the origin,what should you replace?

A: To test for symmetry with respect to origin we replace x by -x and y by -y. If after simplifying the…

Q: Consider the circle with center (h, k) and radius length r. If the circle contains the point (c, d),…

A: Given that the circle with center (h,k) and radius  length  r . Then (c,d) be the point on the…

Q: In the diagram below of circle K, secant PLKE and tangent PZ drawn from external poim are 180'

A: we have given that,  mLZ⏜=56∘ ∠P=?

Q: Given the line segment below, construct a perpendicular bisector to it at the point indicated.

A: We have to draw the perpendicular bisectors for the line at point indicated in problem 2.

Q: Prove that the angle substended by an arc of a circle at the centre is doubled the angle substended…

A: Let O be the center of circle. PQ is an arc subtending ∠POQ at the center O. To prove: ∠POQ=2∠PAQ

Q: (b) Prove that the perpendicular bisector of a chord of a circle passes through the centre.

A:

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A:

Q: Sketch a circle with two noncongruent chords. Is the longer chord farther from the center or closer…

A: Given : To draw the two congruent chords inscribed in a…

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A:

Q: In the given figure, M and N are centres of two intersecting circles which interest at A and B.…

A:

Q: A_______ __________ is a positive angle whose vertex is at thecenter of a circle

A: It is given that, A_______ __________ is a positive angle whose vertex is at thecenter of a circle.

Q: Sketch the torus that results when the given circle of radius length 1 unit is revolved about the…

A: Given: Radius of the circle is 1 unit. Distance between horizontal and center is 4 units. A torus…

Q: Investigate the possibility, given a circle, of drawing two chords whoselengths are in the ratio 1…

A: Given a circle, Draw two chords whose lengths are in the ratio 1:2 and whose distance from the…

Q: 4. The perpendicular offset of the PT of a simple curve is 120.20m. If the angle of intersection is…

A: I am attaching image so that you understand each and every step.

Q: Two congruent intersecting circles B and D (not shown) have a line (segment) of centers BD and a…

A: The figure is drawn as shown in the figure with the give conditions.B and D are the centers of two…

Q: Illustrate Desargues’ Theorem by drawing triangles perspective at a point and showing that they are…

A: We know that, Desargues's theorem holds for projective space of any dimension over any field and…

Q: Construct a line segment tangent to the circle through the point given.

A: In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly…

Q: Prove that if A is a point on the perpendicular bisector of line segment BC then A is the same…

A:

Q: For concentric circles with radii of lengths 3 in. and 6 in., find the area of the smaller segment…

A: Given: Radii of concentric circles: 3 in. and 6 in. Here AB is the tangent to the smaller circle.…

Q: In the accompanying diagram of circle 0, chords AB and CD intersect at E, mĀČ = 50, and %3D mBD =…

A: to find:- angle AED.

Q: Two circles have radius of 4cm and 12 cm respectively. If the distance between their centers is 30…

A:

Q: A total of 250,000 m2 of land is needed to build a nuclear power plant. Suppose it is decided that…

A: Use the formula for the area of circle and length of Arc length of a sector.

Q: A circle is inscribed in a polygon if each side of the polygon is tangent to the circle. true or…

A: If all the vertices of a polygon are on the circumference of a circle, the polygon is inscribed in a…

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Q: Each of the three congruent circles of radius equal to 3 cm is tangent to the other two. Find the…

A: The length of sides of ∆ABC is calculated as follows:

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A:

Q: The side labeled b has been chosen as the base for this parallelogram. Draw a segment showing the…

A: The diagram is shown in the figure represents the parallelogram. One side of the parallelogram is…

Q: A circle is best described as "an oval plane figure."

A: Recall:  All circles can be described as ovals.

Q: Prove that the midpoint of the hypotenuse of a right triangle is. equidistant from the verticle

A: Instead of T,S,V and M I choose C,A,B and D

Q: Consider the parallelogram at right. a What is the length of the base of the parallelogram?

A: We have a parallelogram. To find the length of the base of the parallelogram. Solution: We know…

Q: 1. When two chords of a circle are parallel, are the arcs they intercept be congruent? How about the…

A: Given that two chords of a circle are parallel and the arcs intercept the congruent. The arc that…

Q: A right cone whose base diameter and perpendicular height are 18cm and 8cm respectively is made to…

A: A right cone whose base diameter and perpendicular height are 18cm and 8cm respectively is made to…

Q: Given an acute angle, show that not every point inside the angle lies on a segment of a hyperbolic…

A: Show that not every point inside the angle lies on a segment of a hyperbolic straight line joining…

Q: The length of arc ab of the circle with center at O is equal to twice the length of the radius r of…

A: This question is related to Circle , We will solve it using given information.

Q: The chapter is about other area relationships in a circle such as sector and segment perimeter and…

A: Given that the concentric circles with radii of length 3 inch and 6 inch.   Draw the diagram of the…

Q: Given a sector length of 1 and a chord length of 20, the radius of the circle will be?

A: Given,  Sector length (depicted in figure) = 1unit Chord length = 20  unit Radius of circle = ?…

Q: . Prove that the perpendicular bisector of any chord of a circle passes through its center.

A: we will use method of contradiction i.e., we assume that the perpendicular bisector does not pass…

Q: prove the theorem that states that the angle between a tangent and a chord is equal to the angle in…

A: To prove the theorem that states that the angle between a tangent and a chord is equal to the angle…

Q: 7. The sides of quadrilateral PQRS are tangent to the circle at the points as pictured below. What…

A: Use the property of quadrilateral inscribed a circle.

Q: DA =

A:

Q: 2. In the accompanying diagram of circle 0, PC is a tangent, PBA is a secant, mAB = 132, and mCB -…

A: Given: In the diagram  PC is tangent and PBA is secantmAB⏜=132mCB⏜=46 To find out: ∠P=?

Q: The cross sections of a sphere are circles. TRUE OR FALSE?

A:

Q: Determine if AB is tangent to the circle. 6.6 13 Segment AB 1Select] tangent to the circle becaus 1…

A: AB IS NOT A TANGENT TO THE CIRCLE. Properties of Tangents The tangent line never crosses the…

Q: Find the length (cm) of a common chord of two circles of radii 25 cm and 26 cm respectively, if the…

A:

Q: Show that one slice of an 18-inch pizza is larger than two slices of a 12-inch pizza if cut in eight…

A:

Q: Suppose you use geometry software to construct two chords, RS and TU, that Intersect Inside a circle…

A:

Q: Given a sector length of 1 and a chord length of 2, the radius of the circle (controlled by the…

A: Given- A sector length and chord length is 1 and 2 unit respectively , and the figure is To find-…

Q: 3. Illustrate Desargues' Theorem by drawing triangles perspective at a point, and showing that they…

A: Solution Desargues' theorem :-