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Question
In following fig., ABC is a right- angled triangle at A with sides AB = 5 cm and BC = 13 cm . A circle with centre O has been inscribed in the triangle ABC. Calculate the radius of the incircle.
Solution
In right Δ BAC,
BC2= AC2+ AB2
AC2= 132 -52
AC2 = 169 - 25
AC2 = 144
AC = 12
Let OP = OQ = r (say) (radius of same circle)
∠ OQP = ∠ OPQ = 90° (radius is .L to tangent at the point of contact)
∴ OPAQ is a square.
AQ = AP = OP = OQ = r
BQ = BR = 5 - r ---(1) (length of tangents drawn from an external point)
PC = CR = 12 - r - (2) to a circle are equal}
BC = CR+ BR
13 = 12 - r + 5 - r [from (1) and {2}]
2r = 4
r = 2
Thus , radius of the circle is 2 cm
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