Mathematics
In the adjoining figure, if sides PQ, QR, RS and SP of a quadrilateral PQRS touch a circle at points A, B, C and D respectively, then PD + BQ is equal to
PQ
QR
PS
SR
Circles
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Answer
We know that if two tangents are drawn from an external point to a circle then, the lengths of the tangents are equal.
From figure,
PA and PD are the tangents to the circle from P.
∴ PA = PD
QB and QA are the tangents to the circle from Q.
∴ QB = QA
Hence,
⇒ PD + BQ
⇒ PA + QA
⇒ PQ.
Hence, Option 1 is the correct option.
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