# In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm then perimeter of quad. ABCD isA. 18 cmC. 36 cmB. 27 cmD. 32 cm

As we know Tangents drawn from an external point are equal]

In the given Figure, we have

AP = AS = 6 cm [AP = 6 cm is given]

[ Tangents from point A]

BP = BQ = 5 cm [BP = 5 cm is given]

[ Tangents from point B]

CR = CQ = 3 cm [CQ = 3 cm is given]

[ Tangents from point C]

DR = DS = 4 cm ][DR = 4 cm is given]

[ Tangents from point D]

Now,

Perimeter of ABCD = AB + BC + CA + DA

= AP + BP + BQ + CQ + CR + DR + DS + AS

= 6 + 5 + 5 + 3 + 3 + 4 + 4 + 6 = 36 cm

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