Multiple choice

If ?ABC is right angled at B with AB=12 cm and AC=13 cm, then the radius of the circle inscribed in this triangle is

  1. 2.5 cm

  2. 3 cm

  3. 2 cm

  4. 3.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In right triangle ABC with right angle at B, AB = 12, AC = 13. Using Pythagorean theorem: BC = √(13^2 - 12^2) = √(169 - 144) = √25 = 5. For a right triangle, inradius r = (a + b - c)/2 where c is hypotenuse. Here r = (12 + 5 - 13)/2 = 4/2 = 2 cm. Alternatively, r = Area / semi-perimeter = (1/2 × 12 × 5) / ((12+5+13)/2) = 30 / 15 = 2.

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