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.StatementReason TO PROVE THAT A QUADRILATERAL IS CYCLICTheorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of thesetheorems 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 4Be• +X = 180°Given:Quadrilateral ABCD with B+D=180°Conclusion: ABCD is a cyclic quadReason:opp Zs of quad supplCONVERSE OF THEOREM 5If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral iscyclic.BDEGiven:Quadrilateral ABCD with BC extended to E. BẬD = EĈD.Conclusion: ABCD is a cyclic quadext Z of quad = opp int ZReason:CONVERSE OF THEOREM 6If a line segment joining two points subtends equal angles at two points on the same side of the linesegment, then the four points are concyclic.BBGiven:Four points A, B, C and D with A and D on the same side of BC. BÁC= BDCConclusion: ABCD is a cyclic quadline subtends = ZsReason:53

Here first theorem will be used that is Sum of Opposite angles in a cyclic quadrilateral is…

Answered: In the following sketch, O is the…

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.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter4: Quadrilaterals

Section4.1: Properties Of A Parallelogram

Problem 23E: In quadrilateral RSTV, the midpoints of consecutive sides are joined in order. Try drawing other...

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Question

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

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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