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Question
ABC is a right angles triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.
Calculate the value of x, the radius of the inscribed circle.
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Solution
In ΔABC, ∠B = 90°
OL ⊥ AB, OM ⊥ BC and ON ⊥ AC
LBNO is a square
LB = BN = OL = OM = ON = x
∴ AL = 12 – x
∴ AL = AN = 12 – x
Since ABC is a right triangle
AC2 = AB2 + BC2
`=>` 132 = 122 + BC2
`=>` 169 = 144 + BC2
`=>` BC2 = 25
`=>` BC = 5
∴ MC = 5 – x
But CM = CN
∴ CN = 5 – x
Now, AC = AN + NC
13 = (12 – x) + (5 – x)
13 = 17 – 2x
2x = 4
x = 2 cm
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