Question

CBSE CLASS X

Circles - Mathematics

Answer 1

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Answer 2

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You can refer the given attachment :)

Given :-

ABCD is a Quadrilateral circumscribing the circle with centre O.
Sides of the quadrilateral touch the circle at the points P, Q, R and S.


To prove :-

AB + CD = BC + DA


Proof :-

We know the theorem that ,

Length of the Tangents drawn from external points are equal.

Thus,

We can say that,

Seg DR = Seg DS .. eq(1)
CR = CQ .. eq(4)
BP = BQ .. eq(3)
AP = AS .. eq(2)

Let's add the eq(1), eq(2), eq(3), eq(4)

DR + CR + BP + AP = DS + CQ + BQ + AS

Now,
D-R-C , C-Q-B , A-P-B , D-S-A

So,

DC + AB = AD + BC

Hence,

AB + CD = BC + DA

Hence , Proved.

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