Question

prove that a rectangle circumscribed with a circlr is a spuare

Answer 1

Given:
A rectangle ABCD circumscribe 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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