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ICSE Class 9 Answered

In ∆ ABC, AB = AC and the bisectors of angles B and C intersect at point O. Prove that  I) BO = CO  ii) AO bisects angle BAC
Asked by Vinutham71 | 19 Jun, 2018, 10:37: PM
answered-by-expert Expert Answer
begin mathsize 16px style Proof colon left parenthesis straight i right parenthesis space To space prove space that space colon space BO thin space equals space CO space AB space equals space AC space.... given rightwards double arrow angle straight B space equals space angle straight C space...... space angles space opposite space to space equal space sides space of space straight a space triangle space are space equal rightwards double arrow 1 half angle straight B space equals space 1 half angle straight C rightwards double arrow angle OBC space equals space angle OCB space space space....... left parenthesis since space BO thin space and space OC space are space the space bisectors space of space angle straight B space and space angle straight C right parenthesis rightwards double arrow OB space equals space OC rightwards double arrow BO space equals space CO left parenthesis space sides space oppsite space to space equal space angles space of space straight a space triangle space are space equal right parenthesis left parenthesis ii right parenthesis space In space increment OAB space and space increment OAC comma AB space equals space AC space... space given OA space equals space OA space...... common space side BO space equals space CO space...... space proved space in space left parenthesis straight i right parenthesis rightwards double arrow increment OAB space approximately equal to space space increment OAC space space space space.... space by space SSS space Test rightwards double arrow angle OAB space equals space angle OAC space............. straight C. straight P. straight C. straight T rightwards double arrow AO space bisects space angle space BAC end style
Answered by Yasmeen Khan | 20 Jun, 2018, 11:48: AM

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