Prove that rectangle circumscribing a circle is a square

Asked by admin @ 16/08/2021 in Math viewed by 352 People

Prove that a rectangle circumscribing a circle is a square

Answered by admin @ 16/08/2021

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
Brainliest please
Thanks

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