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Class 10
Mathematics
Circles
a quadrilateral abcd is drawn to circumscribe a ci...

Question:
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

Answer:

Given : A quadrilateral ABCD which circumscribe a circle .

To prove: AB + CD = AD + BC

Proof: As we know tangents drawn from external point are equal. Therefore, we have

DR = DS …………….. (1)

AP = AS ……………… (2)

PB = BQ ……………… (3)

CR = CQ ………………. (4)

Adding equation (1), (2), (3) and (4), we get

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

AB + CD = AD + BC

Hence proved.

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Question:
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

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Question: A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

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Question:
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC