Q. 385.0( 1 Vote )

# In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm and CS = 3 cm. Then, the length AB = ? A. 9 cmC. 12 cmB. 10 cmD. 8 cm

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

In the given Figure, we have

AP = AQ = 5 cm

[Tangents from point A] [AP = 5 cm is given]

BQ = BR = x(say)

[Tangents from point B]

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

[Tangents from point C]

Given,

BC = 7 cm

CR + BR = 7

3 + x = 7 cm

x = 4 cm

Now,

AB = AQ + BQ = 5 + x = 5 + 4 = 9 cm

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