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Question

# Consider two right-angled triangles inscribed in a square such that their hypotenuse intersect at a point O inside the square. What is the angle between the hypotenuse of the triangle and the base of the square?

A

30

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B

90

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C

45

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D

60

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Solution

## The correct option is C 45∘ In the square ABCD, we have right-angled triangles, △ ADC and △ BCD such that their hypotenuse intersect at the point O inside the square. Now, since the diagonals of a square are equal in length, and every angle is a right angle, we have BD=AC and ∠B=90∘. Thus, △BDC is a right-angled isosceles triangle. ⟹∠BDC=45∘ .....(Sum of angles of a triangle is 180∘)

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