If the bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is

(a) 45°

(b) 95°

(c) 135°

(d) 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 .

Now, using the angle sum property of a triangle

In ΔABC

Now, further multiplying each of the term by in (1)

Also, applying angle sum property of a triangle

In ΔAOC

Thus,

Therefore, the correct option is (c).

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