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Question
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
Options
45°
95°
135°
90°
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Solution
In the given problem, bisectors of the acute angles of a right angled triangle meet at O. We need to find ∠AOC.
Now, using the angle sum property of a triangle
In ΔABC
∠A + ∠B + ∠C = 180°
90° + ∠A+ ∠C = 180°
∠A + ∠C = 90° ..............(1)
Now, further multiplying each of the term by 1/2in (1)
`1/2 ∠A + 1/2 ∠C = 1/2 90°`
∠OAC + ∠ACO = 45°
Also, applying angle sum property of a triangle
In ΔAOC
∠OAC + ∠ACO + ∠AOC = 180°
45° + ∠AOC = 180°
∠AOC = 180° - 45°
= 135°
Thus, ∠AOC = 135°
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