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Q.

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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a

24 cm

b

23 cm

c

22 cm 

d

26 cm

answer is A.

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Detailed Solution

Given that △ABC   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 ABC,A C 2 =A B 2 +B C 2   where AC  is the hypotenuse of △ABC  .
Question ImageIn triangle ABC,
BC 2 =AC 2 +AB 2 ⇒BC= 24 2 +10 2 ⇒BC= 576+100 ⇒BC= 676   Therefore, BC=26 cm.
Hence, option 1 is correct.
 
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