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A quadrilateral ABCD is drawn to …

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A quadrilateral ABCD is drawn to circumscribe a circle prove that AB + CD is equals to ad + Bc

Posted by Vinay Waldia Waldia 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 3 months ago

Since, tangents drawn from an exterior point to a circle are equal in length.

∴ AP = AS    ...(i)
BP = BQ    ...(ii)
CR = CQ    ...(iii)
and DR = DS    ...(iv)
Adding (i), (ii), (iii) and (iv), we get
AP + BP + CR + DR = AS + BQ + CQ + DS
⇒ (AP + BP) + (CR + DR)
= (AS + DS) + (BQ + CQ)
⇒ AB + CD = AD + BC
Hence, AB + CD = BC + DA.

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