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  • Bisectors of the angles B and C of an isosceles triangle ABC with AB equal to AC intersect each other at O. Show that external angle adjacent to angle ABC is equal to angle BOC

Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that the external angle adjacent to \angleABC is equal to \angleBOC

Answers (1)

Given, that ABC is an isosceles triangle

 and, AB = AC

To prove: External angle adjacent to \angleABC is equal to \angleBOC

Proof: Produce line CB to D in \triangleABC

AB = AC                     (Given)

\angleACB = \angleABC          (angles opposite to equal sides are equal)

\angleOCB = \angleOBC          (Bisector of angle B and C, respectively)

In \triangleBOC,  

\angleOBC + \angleOCB + \angleBOC = 180°

\Rightarrow 2\angleOBC + \angleBOC = 180°   (From above)

\Rightarrow \angleABC + \angleBOC = 180°

(\because  \angleABO + \angleOBC = \angleABC)

\Rightarrow \angleABC+ \angleOBA = 180°

\Rightarrow \angleOBA = \angleBOC.

Hence proved.

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