a quadrilateral ABCD is drawn to circumscribe a circle. prove that AB+CD=1/2(AB+BC+CD+AD)
See RS agarwal EXAMPLE SECTION OF CHAPTER CIRCLE
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A quadrilateral ABCD is drawn to circumscribe a circle prove that AB + CD is equals to ad + Bc
A quadrilateral ABCD is drawn to circumscribe a circle prove that AB + CD is equals to ad + Bc
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that : AB +CD = AD+BC
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that : AB +CD = AD+BC
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We know that the tangent segments from an external point to a circle are equal\xa0{tex}\\therefore{/tex} AP = AS ……..(1)BP = BQ …….(2)CR = CQ …….(3)DR = DS …….(4)Adding (1), (2), (3) and (4), we get(AP + BP) + (CR + DR) = (AS + BQ + CQ + DS){tex}\\Rightarrow{/tex}\xa0AB + CD = (AS + DS) + (BQ + CQ){tex}\\Rightarrow{/tex}\xa0AB + CD = AD + BC
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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 getAP + BP + CR + DR = AS + BQ + CQ + DS⇒ (AP + BP) + (CR + DR)= (AS + DS) + (BQ + CQ)⇒ AB + CD = AD + BCHence, AB + CD = BC + DA.