Math, asked by arpit8660, 1 year ago

in the adjoining figure triangle ABC is an equilateral triangle. Bisector of angle B intersects circumcircle in point p. Prove that cq=ca

Answers

Answered by morankarmanohar
62

Step-by-step explanation:

AB = AC

ACB =ABC ..........1

ACB is exterior angle of triangle AQC

ACB=QAC+AQC

ABC=QAC+AQC ........from 1 ....2

Now ABP=PBC.....angle B is bisector

2PBC=ABC

hence, 2 PBC = QAC + AQC.......from 2.....3

PAC = PBC ...... tangent secant theorem.......4

hence, PBC = AQC ..........5

2 PBC = PBC + AQC ....... from 3 and 5

PBC = AQC

PAC = AQC ......from 4

QAC = AQC

Therefore, CQ = CA ..... side opposite to equal sides are equal.

HENCE PROVED

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