Class 9

Math

All topics

Conic Sections

In any triangle ABC, if the angle bisector of $∠A$and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

from diagram

$∠BAD=∠CAD$

so, ABD is a Cyclic Quadrilateral

$∠DBC=∠DAC=21 ∠A$

$∠DCB=∠BAD=21 ∠A$

$∠DBC=∠DCB$

$In△DCB$

BP and CD are equal

D lies on perpendicular bisector of BC