Question

A circle is inscribed within a quadrilateral ABCD touching the sides AD, AB, BC and CD at points P, Q, R and S respectively. If BC = 14 cm, BQ = 8 cm and DC = 18 cm and AD perpendicular to DC, then find the radius of the circle.​

Answer 1

Answer:

∵ Lengths of tangents drawn from an external point to a circle are equal.

∴BQ=BR=27 cm

Let x be the radius of the circle

∴OP=OS=PD=x

Now,

CR=BC−BR

=38−27=11 cm

Now CS=CR=11 cm

[∵ Length of tangents from an external point to a circle are equal]

∴DS=CD−CS

=25cm−11 cm

=14 cm

But DS=OP=x=14 cm.

Hence radius =OP=14 cm,

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