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(g) In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral.

(g) In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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theorems are used to prove that a given quadrilateral is cyclic. LO PROVE THAT A QUADRILATERAL IS CYCLIC oroms 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these CONVERSE OF THEOREM 4 cabe opposite angles of a quadriılateral are supplementary, then the quadrilateral is cyclic. B • +X = 180° Quadrilateral ABCD with ÊB+D=180° Given: Conclusion: ABCD is a cyclic quad Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. D B BK Given: Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Conclusion: ABCD is a cyclic quad Reason: ext Z of quad = opp int 2 CONVERSE OF THEOREM 6 a mie segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. 1D B our points A, B, C and D with A and D on the same side of BC. BẬC= BI C Reason: Given: Conclusion: ABCD is a cyclic quad line subtends = Zs 53
Transcribed Image Text:theorems are used to prove that a given quadrilateral is cyclic. LO PROVE THAT A QUADRILATERAL IS CYCLIC oroms 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these CONVERSE OF THEOREM 4 cabe opposite angles of a quadriılateral are supplementary, then the quadrilateral is cyclic. B • +X = 180° Quadrilateral ABCD with ÊB+D=180° Given: Conclusion: ABCD is a cyclic quad Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. D B BK Given: Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Conclusion: ABCD is a cyclic quad Reason: ext Z of quad = opp int 2 CONVERSE OF THEOREM 6 a mie segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. 1D B our points A, B, C and D with A and D on the same side of BC. BẬC= BI C Reason: Given: Conclusion: ABCD is a cyclic quad line subtends = Zs 53
() In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral. Statement Reason
Transcribed Image Text:() In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral. Statement Reason
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