1.(i) In an isosceles triangle ABC, with \small AB=AC, the bisectors of \small \angle B and \small \angle C intersect each other at O. Join A to O. Show that :

 (i) \small OB=OC

Answers (1)

In the triangle ABC,

Since AB  =  AC, thus        \angle B\ =\ \angle C

or                                        \frac{1}{2}\angle B\ =\ \frac{1}{2}\angle C

or                                      \angle OBC\ =\ \angle OCB      (Angles bisectors are equal)

Thus       \small OB=OC   as sides opposite to equal are angles are also equal.

 

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