Question

O is centre of a circle which has two chords BA and BC with point B on the circumference of the circle.
If OB bisects angle ABC,
prove that AB=AC

Answer 1

\[\Large \triangle BOC, \;\triangle BOA\] are isosceles triangles

\[\Large \angle OBC \cong \angle OCB,\; \angle OBA \cong \angle OAB\]

\[\Large \angle OCB \cong \angle OAB\] by transitive property

\[\Large \triangle BOC \cong \triangle BOA\] by AAS congruence

\[\Large \overline {BC} \cong \overline{BA} \] as corresponding parts

Answer 2

we need to show AB=AC ? Is the ques right?

Answer 3

yes

Answer 4

just by the look of it, doesn;t seem right?