The bisector of angle B of an isosceles triangle ABC with AB=AC meets the circumcircle of triangle ABC at P .If AP and BC produced meet at Q then prove that CQ=CA.
Answers
Answered by
10
triangle ABC is isosceles, with angle B = angle C
Call the bisected angle at B = x (so angle B and angle C are both 2x)
use these theorems:
angle at Q formed by 2 secants = (angle of outer arc - angle of inner arc)/2
in other words angle Q= ( arc AB - arc PC)/2
also, inscribed angle PBC = (arc PC)/2. that is, x= arc PC /2
similarly 2x = arc AB/2
Answered by
2
Answer:
Step-by-step explanation:
Attachments:
Similar questions