19.Prove that the rectangle circumscribing a circle is a square.ndrant

1.	19.Prove that the rectangle circumscribing a circle is a square.ndrant of a circle of radius 14 cm and a semicir
Answer» 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+QCAB +CD=AD+BC2AB =2BCAdjacent sides are equal so ABCD is a square.

19.Prove that the rectangle circumscribing a circle is a square.ndrant of a circle of radius 14 cm and a semicir

Answer»

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+QCAB +CD=AD+BC2AB =2BCAdjacent sides are equal so ABCD is a square.