Prove that the rectangle circumscribing a circle is a square.
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ABCD is a square
Step-by-step explanation:
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
AB +AB = AD+AD
2AB = 2 AD
AB = AD
so, AB= AD, AB=CD , AD=BC
SO, AB=BC=AD=CD
hence, ABCD is a square
#Learn more:
Draw inscribed circle and circumscribed circle in the triangle
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