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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