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In the following sketch, O is the centre of the. circle. BC is a tangent to the circle at B. 12 Prove that AOBC is a cyclic quadrilateral.

In the following sketch, O is the centre of the. circle. BC is a tangent to the circle at B. 12 Prove that AOBC is a cyclic quadrilateral.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section: Chapter Questions
Problem 1GP: The diagram shown in Figure 1 was used by the Hindu mathematician Bhaskara to prove the theorem in...
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Please help me with this question by using one of these three theorems in picture 1.
A In the following sketch, O is the centre of the. circle. BC is a tangent to the circle at B. 2. Prove that AOBC is a cyclic quadrilateral. Statement Reason
Transcribed Image Text:A In the following sketch, O is the centre of the. circle. BC is a tangent to the circle at B. 2. Prove that AOBC is a cyclic quadrilateral. Statement Reason
TO PROVE THAT A QUADRILATERAL IS CYCLIC Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these theorems are used to prove that a given quadrilateral is cyclic. If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. CONVERSE OF THEOREM 4 Be • +X = 180° Given: Quadrilateral ABCD with B+D=180° 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. B D E Given: Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Conclusion: ABCD is a cyclic quad ext Z of quad = opp int Z Reason: CONVERSE OF THEOREM 6 If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. B B Given: Four points A, B, C and D with A and D on the same side of BC. BÁC= BDC Conclusion: ABCD is a cyclic quad line subtends = Zs Reason: 53
Transcribed Image Text:TO PROVE THAT A QUADRILATERAL IS CYCLIC Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these theorems are used to prove that a given quadrilateral is cyclic. If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. CONVERSE OF THEOREM 4 Be • +X = 180° Given: Quadrilateral ABCD with B+D=180° 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. B D E Given: Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Conclusion: ABCD is a cyclic quad ext Z of quad = opp int Z Reason: CONVERSE OF THEOREM 6 If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. B B Given: Four points A, B, C and D with A and D on the same side of BC. BÁC= BDC Conclusion: ABCD is a cyclic quad line subtends = Zs Reason: 53
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