Prove that rectangle circumscribing a circle is square
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Answer with Step-by-step explanation:
ABCD is a rectangle
AB=CD, BC=AD
Angle A=Angle B=Angle C=Angle D=90 degrees
To prove that
AB=BC=CD=AD
Proof: AB, BC,CD and AD touch the circle at point P,Q,R and S
Tangents drawn from external point are equal.
AP=AS...(1)
PB=BQ...(2)
CR=QC..(3)
DR=DS..(4)
Adding (1), (2),(3) and (4)
Then, we get AP+PB+CR+DR=AS+BQ+QC+DS
AB+CD=AD+BC
AB+AB=BC+BC
2AB=2BC
AB=BC
When AB=CD and AB=BC
And BC=AD
Then, AB=BC=CD=AD
Hence, rectangle circumscribing a circle is a square.
#Learns more:
https://brainly.in/question/285872:Answered by NikhilMTomy
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