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प्रश्न
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.
उत्तर
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 △ABC = area of △APB + area of △BPC + area of △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 + 12 xx 6 xx r + 12 xx 10 xx r`
24 = 4r + 3r + 5r
24 = 12r
⇒ r = 2
∵ d = 2r
⇒ d = 2 x 2
⇒ d = 4 cm.
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