Question
In the figure given below, a circle is inscribed in a
triangle ABC. If AB = 18 cm, BC = 14 cm and AC = 16 cm, then find the length of YC.Solution
ATQ,
Let YA = 'a' cm
YC = AC - YA = (16 - a) cm
We know that the tangents drawn from an external point to a circle are equal.
So, ZC = YC = (16 - a) cm
BZ = BC - ZC = 14 - (16 - a) = (a - 2) cm
Again, BX = BZ = (a - 2) cm
AX = AB - BX = 18 - (a - 2) = (20 - a) cm
Again, AX = YA
So, 20 - a = 'a'
Or, 2a = 20
Or, 'a' = 10
Therefore, YC = 16 - 10 = 6 cm
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