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Q.

Choose whether the given statement is true or false.

A circle touches all the four sides of a quadrilateral ABCD . So, AB+CD=BC+DA.

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a

True

b

False

answer is A.

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Detailed Solution

Question Image

To prove: AB + CD = BC + DA
Proof:
We know that tangents drawn from an external point to a circle are equal.
So, AP=AS,
BP=BQ,
CQ=CR,
DR=DS.
L.H.S. = AB + CD
= AP + PB + CR + RD
= AS + BQ + CQ + DS
(Tangents from same external point are always equal)
= (AS + SD) + (BQ + QC)
= AD + BC
= R.H.S.
Hence Proved.
So, the given statement is true.

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Choose whether the given statement is true or false.A circle touches all the four sides of a quadrilateral ABCD . So, AB+CD=BC+DA.