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Question
In Fig. 4, a circle is inscribed in a ΔABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the lengths BL, CM and AN.
Solution
BN and BL are tangents from the same point to the circle
∴ BN = BL
Similarly
AM = AN and CL = CM
Given that
AB = 10 cm, BC = 8 cm and AC = 12 cm
Let
AN = AM = x
CM = CL = y
BN = BL = z
AB + AN + NB = 10
BC = BL + LC = 8
AC = AM + MC
=
Adding equations (1), (2) and (3), we get
2 (x + y + z) = 30
⇒ x + y + z = 15 ...(4)
Subtracting (1) from (4) we get
y = 5
Subtracting (2) from (4) we get
x = 7
Subtracting (3) from (4) we get
z = 3
BL = z = 3 cm
CM = y = 5 cm
AN = x = 7 cm
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