7. INVESTIGATE In the sketch O is the centre of the circle and C and ɓ are angles in segment AB of the circle (or: angles subtended by chord AB). D Prove that C-D. (Do not measure C and D, but use knowledge of Geometry facts and theorems to show why C-D.) Hint: Draw in AO and BO In the sketch below ABCD is a cyclic quadrilateral, ie a quadrilateral with all four of its sides chords of the circle. Measure each of the angles A B- 6- A Complete 180 and also: 180 Therefore: The angles of a cyclic 131 C D B quadrilateral are In the sketch PQRS is a cyclic quadrilateral. O is the centre of the circle and QO and OS are drawn Complete the following proof, also giving reasons for statements where required. 0,-2-angle [Reason: 161 R 0,-2-angle [Reason: ..0,+0,-2x angle +2xangle. s Also: Ò,+0, [Reason: 2x angle +2xangle angle +angle 171

7. INVESTIGATE In the sketch O is the centre of the circle and C and ɓ are angles in segment AB of the circle (or: angles subtended by chord AB). D Prove that C-D. (Do not measure C and D, but use knowledge of Geometry facts and theorems to show why C-D.) Hint: Draw in AO and BO In the sketch below ABCD is a cyclic quadrilateral, ie a quadrilateral with all four of its sides chords of the circle. Measure each of the angles A B- 6- A Complete 180 and also: 180 Therefore: The angles of a cyclic 131 C D B quadrilateral are In the sketch PQRS is a cyclic quadrilateral. O is the centre of the circle and QO and OS are drawn Complete the following proof, also giving reasons for statements where required. 0,-2-angle [Reason: 161 R 0,-2-angle [Reason: ..0,+0,-2x angle +2xangle. s Also: Ò,+0, [Reason: 2x angle +2xangle angle +angle 171

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of...

See similar textbooks

Similar questions

a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
Which types of quadrilaterals is are necessarily cyclic? a A kite b A rectangle
Given that mAC:mBC:mAB=4:3:2 in circle O: a Which arc is largest? b Which chord is longest?
a Does the similarity relationship have a reflexive property for triangles and polygons in general? b Is there a symmetric property for the similarity of triangles and polygons? c Is there a transitive property for the similarity of triangles and polygons?
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RT
a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter? b Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?
The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent AB? HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Which of these two polyhedrons is concave? Note that the interior dihedral angle formed by the planes containing EJF and KJF is larger than 180 .
Given that rectangle ABCE is similar to rectangle MNPR and that CDEPQR, what can you conclude regarding pentagon ABCDE and pentagon MNPQR?
What type of trapezoid a has congruent diagonals. b has congruent base angles.
For rectangle MNPQ, points A, B, C and D are the midpoints of the sides. aWhat type of quadrilateral not shown is ABCD? bAre the inscribed circle for ABCD and the circumscribed circle for MNPQ concentric circles?