Question

in the given figure, a circle is inscribed in quad. ABCD .if BC=38cm,BQ=27cm,DC=25 cm and AD perpendicular to DC find the radius of the circle.
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Answer 1

Answer:

From the given figure we see that,

∵ BQ = BR = 27

= As BC = 38 cm

∴CR =CB -BR =

38 - 27

= 11cm

Again ,

∵CR =CS =11cm

∴now ,

as DC = 25 cm

DS =DC - SC

= 25 - 11 = 14cm

∴Now ,

= In quadrilateral DSOP ,

∠PDS = 90°( given )

∠OSD = 90° , ∠OPD = 90°

DSOP is a parallelogram

OP ∥ SD and PD ∥ OS

∴Now ,

as OP = OS

OPDS is a square .

DS =OP=14 cm

➡Radius of the circle = 14 cm