A circle is inscribed inside a right-angled triangle. If BC = a, CA= b and AB = c, then the radius of the circle is ____.
(a+b−c)2
The triangle ABC is drawn as described in the question. D.E and F are the points of contacts of the tangents.
OECD is a square.
OE=OD= CD = CE = r, where r is the radius of the circle.
BE = a - r
BE = BF = a - r ..... (tangents froman external point are equal)
AD = b - r
AD = AF = b - r ..... (tangents froman external point are equal)
We know that BA = BF + FA
c = b - r + a - r
2r = a + b - c
r = (a+b−c)2