Question

prove that the rectangle circumscribing a circle is a square​

Answer 1

Given:

A rectangle ABCD curcumscribe a circle which touches the circle at P, Q, R, S.

To Prove:

ABCD is a square.

Proof:

As tangents from external point are equal.

AP = AS−−−−−−−−−−−(1)

PB = BQ −−−−−−−−−−(2)

DR = DS−−−−−−−−−−(3)

RC = QC−−−−−−−−−−(4)

Add (1), (2), (3) and (4)

AP+PB+DR+RC = AS +BQ+DS+QC

AB +CD=AD+BC

2AB =2BC

Adjacent sides are equal so ABCD is a square.

Hope it helps

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