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Question
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.
Solution
We have given that a circle is inscribed in a triangle
Using pythagoras theorem
`(AC)^2 = (AB)^2 + (BC)^2`
`(AC)^2 = (8)^2 + (6)^2`
`(AC)^2 = 64 + 36`
`(AC)^2 = 100`
⇒ AC = 10
Area of Δ ABC = area of Δ APB + area of Δ BPC + area of Δ APC
`1/2 xx b xx h = 1/2 xx b_1 xx h_1 + 1/2 xx b_2 xx h_2 + 1/2 xx b_3 xx h_3`
`1/2 xx 6 xx 8 = 1/2 xx 8 xx r + 1/2 xx 6 xx r + 1/2 xx 10 xx r`
`24 = 4r + 3r + 5r`
`24 = 12r`
⇒ r = 2
∵ d = 2r
⇒ `d = 2 xx 2`
⇒ d = 4 cm
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