Circles ncert solutions Chapter 10 Exercise 10.2 Question 11
11. Prove that the parallelogram circumscribing a circle is a rhombus.
Solution:
Given: PQRS is a parallelogram circumscribing a circle.
To Prove: PQRS is a rhombus
Proof:
Note: A parallelogram with all equal sides is rhombus. Therefore, if we can prove that all the sides of PQRS are equal then it means its a rhombus.
PQ =SR and QR = SP {Opposite sides of parallelogram are equal} (1)
AP = PB (2)
CQ=BQ (3)
RC=RD (4)
AS = SD (5)
Adding (2), (3), (4) and (5), we get
Putting (1) in the above equation, we get
(6)
From (1) and (6), we can say that
which means PQRS is a rhombus.
Hence Proved
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