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