Q. 164.6( 19 Votes )

In Fig. 4, a circ

Answer :

Let AN = x cm, CM = z cm and BL = y cm


As we know that,


Tangents from an external point to a circle are equal,


In given Figure we have


AN= AM = x [Tangents from point A]


BN = BL = y [Tangents from point B]


CL = CM = z [Tangents from point C]


Now, Given: AC = 12 cm


AM + MC = 12


x + z = 12


z = 12 – x…. [1]


and BC = 8 cm


BL + LC = 8


y + z = 8


z = 8 – y …… [2]


and


AB = 10 cm


AN + BN = 10


x + y = 10 …. [3]


equate [1] and [2] to get,


12 – x = 8 – y


4 = x - y … [4]


Add [3] and [4] to get,


x + x + y – y = 10 + 4


2x = 14


x = 7 cm


put value of x in [4] to get,


4 = 7 – y


y = 3 cm


put value of y in [2] to get,


z = 8 – 3


= 5 cm


Hence,


AN = 7 cm


CM = 5 cm


BL = 3 cm


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