11. Prove that the parallelogram ci...

11. Prove that the parallelogram circumscribing a circle is a rhombus.

JEE/Engineering Exams
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ABCD be a parallelogram uircumscri a iicle with centre 0 Given - bing is a To puone: Rhom bus. Isof: We know the tangents dearsn to a circle fom an entecioc point are equal in length ( therefore A P=A S, B P=B Q, C R=C Q, D R=D S ) AdLerg all aboue ( =13 ) ( A P+B P+C R+D R=A S^{prime}+B 9+C O+D S ) [ begin{array}{l} A P+B P)+(C R+P B)=(A S+D S)+(B Q+(theta) A B+C D=A D+B C 2 A B=2 B C end{array} ] ( A S quad A B C D ) g ( A B=D ) and ( A D=B C ) : ( A B=B C ) [ A B=B C=omega C=A D ] ABCD in rhombus
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