A circle is inscribed in a right-angled triangle with legs of length 5 and 12. What is the area of the quadrilateral formed by the two legs and the two radii to the tangent points on the legs?
Show answer & explanation
Correct answer: A
Explanation
Sides of right triangle = 5, 12 ⇒ Hypotenuse = 13
According to the formula:
Radius of incircle r = (a + b − c)/2
Area of quadrilateral = r²
r = (5 + 12 − 13)/2= 2
Area = r²= 2²= 4