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A quadrilateral ABCD is drawn to circumscribe a circle. If AB =12 cm, BC = 15 cm and CD = 14 cm, find AD. |
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Answer» <P>Answer: Given: Let ABCD is a quadrilateral which circumscribe the circle with CENTER 'O'. The quadrilateral ABCD touches circle at point P , Q , R and S. To proof: AB+CD = AD+BC Proof: AP=AS…(i) BP=BQ…(ii) CR=CQ…(III) DR=DS…(iv) Adding equation (i),(ii),(iii) and (iv) we get… AP+BP+CR+DR=AS+BQ+CQ+DS According to FIGURE [AB=AP+PB, AD=AS+SD, CD=DR+CR, BC=BQ+CQ] Or, AB+CD=AD+BC (Proved). In this question a quadrilateral ABCD is drawn to circumscribe a circle. Hence, AB+CD=AD+BC Or, 12+14=AD+15 Or, AD = 11 cm |
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