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Question
∆LMN is a right angled triangle with ∠L = 90°. A circle is inscribed in it. The lengths of the sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.
Solution
LN = 6; ML = 8.
In the right ∆LMN,
MN2 = LN2 + LM2
= 62 + 82 = 36 + 64 = 100
MN = `sqrt(100)` = 10
OA = OB = OC = r
AN = CN ...(Tangent of the circle)
LN – AL = CN
LN – r = CN
8 – r = CN ...(1)
MC = MB ...(Tangent of the circle)
MC = ML – LB
MC = 6 – r ...(2)
Add (1) and (2)
MC + CN = (6 – r) + (8 – r)
MN = 14 – 2r
10 = 14 – 2r
2r = 14 – 10 = 4
r = `4/2` = 2 cm
radius of the circle = 2 cm
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