8. A quadrilateral ABCD is drawn to circumnscribe a circle (see Fig. 1 – InterviewSolution

1.

8. A quadrilateral ABCD is drawn to circumnscribe a circle (see Fig. 10.12). Pruve thtAB + CD-AD +BCX'Y'Fig. 10.12Fig. 10.13

Answer»

AB+CD=AD+BC

Proof :

AP=AS

PB=BQ

CQ=CR

RD=DS (the length of tangent drawn from an external point to a circle are equal)

AP+PB+RD+CR=AS+BQ+DS+CQ

=>AB+CD=AD+BC

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