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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
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