ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find BC.

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24 cm

23 cm

22 cm

26 cm

answer is A.

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Detailed Solution

Given that

△ A B C

is a right-angle triangle and a circle is inscribed in it.
We have to find the radius of the in-circle.
By Pythagoras theorem, for a right-angle triangle

A B C, A C 2 = A B 2 + B C 2

where AC is the hypotenuse of

△ A B C

In triangle ABC,

BC 2 =AC 2 +AB 2 ⇒ BC= 242 +10 2 ⇒ BC= 576+100 ⇒ BC= 676

Therefore, BC=26 cm.
Hence, option 1 is correct.

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