Q. 25.0( 3 Votes )

The picture shows

Answer :

Let us label the diagram.



As we know that


Tangents from an external point to a circle are equal,


In given Figure we have


AP = AR = x [Tangents from point A]


BP = BQ = y [Tangents from point B]


CQ = CR = z [Tangents from point C]


Now, Given


AB = 4 cm


AP + BP = 4


x + y = 4


y = 4 - x …[1]


and BC = 7 cm


BQ+ QC = 7


y + z = 7


4 - x + z = 7 [From 1]


z = x + 3 …[2]


and


AC = 5 cm


AR + CR = 5


x + z = 5 [From 2]


x + x + 3 = 5


2x = 2


x = 1 cm


Putting value of x in [1] and [2]


y = 4 - 1 = 3 cm


z = 1 + 3 = 4 cm


So, we have


AP = AR = 1 cm


BP = BQ = 3 cm


CQ = CR = 4 cm


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