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  • In ?ABC,AD and CE are the bisectors of angle A and angle C respectively.AD and CE intersect at O.If Angle ABC=90°,then find angle AOC.

In ?ABC,AD and CE are the bisectors of angle A and angle C respectively.AD and CE intersect at O.If Angle ABC=90°,then find angle AOC.

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As we can see from the figure given above
angle AOC= Exterior angle of traingle AOE
Rightarrow angle EAO+angle AEO
Rightarrow fracA2+Exterior, angle, of, traingle, EBC
Rightarrow fracA2+B+fracC2=B+frac(A+B)2
Rightarrow 90+frac902=135^circ
Rightarrow A+B=90, as, ABC, is, a, right, angled, triangle

Posted by

Deependra Verma

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