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