Multiple choice

The in-radius and circum-radius of a right angle triangle are 3cm and 12 cm respectively. Find the Area of triangle.

  1. $84 cm2$
  2. $72 cm2$
  3. $80 cm2$
  4. $81 cm2$
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D Correct answer
Explanation

For a right triangle, circumradius R = hypotenuse/2, so hypotenuse = 24 cm. Inradius r = (a+b-c)/2 where a,b are legs. Given r=3, we have a+b-24=6, so a+b=30. Using a²+b²=24²=576 and (a+b)²=900, we get 2ab=324, so ab=162. Area = ab/2 = 81 cm².

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