Question

. In the figure, quadrilateral ABCD is circumscribing a circle with centre O. Side AB touches the circle at P, BC at Q,

CD at R and AD at S. AD is perpendicular to AB. If the radius of the circle is 10 cm, CR = 27 cm, BC = 38 cm then find

the value of x where x is side AB.​

Answer 1

Answer:

ABCD is a quadrilateral and let O be the center of the circle inscribed in the quadrilateral.

AB, BC, CD and AD are the tangent to the circle at P, Q, R and S, AP=9, PB=7, QC=5 and DR=6

We know that the lengths of the two tangents from a point to circle are equal.

Thus, AP=AS=9 cm

           BP=BQ=7 cm

           CQ=CR=5 cm

           DR=DS=6 cm

Perimeter of quadrilateral ABCD=AB+BC+CD+AD

                                                           =AP+BP+BQ+CQCR+DR+DS+AS

                                                           =9+7+7+5+5+6+6+9

                                                           =54 cm

Answer 2

Answer:

ABCD is a quadrilateral and let O be the center of the circle inscribed in the quadrilateral.

AB, BC, CD and AD are the tangent to the circle at P, Q, R and S, AP=9, PB=7, QC=5 and DR=6

We know that the lengths of the two tangents from a point to circle are equal.

Thus, AP=AS=9 cm

BP=BQ=7 cm

CQ=CR=5 cm

DR=DS=6 cm

Perimeter of quadrilateral ABCD=AB+BC+CD+AD

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

=9+7+7+5+5+6+6+9

-54 cm