In Fig. 8.59, a circle touches all the four sides of a quadrilateral ABCD with AB =6 cm, BC =7 cm and CD =4 cm. Find AD.

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Solution

Sol :
Let P,Q,R,S be the points where the circle touches the quadrilateral .From a point out side of the circle the two tangents to the circle are equal.
AP = AS,BP = BQ , CR = CQ , and DR = DS
Adding AP + BP + CR + DR = AS + BQ + CQ + DS
AB + CD = AD + BC
6 + 4 = AD + 7
AD = 3 cm .

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In Fig. 8.59, a circle touches all the four sides of a quadrilateral ABCD with AB =6 cm, BC =7 cm and CD =4 cm. Find AD.

Sol : Let P,Q,R,S be the points where the circle touches the quadrilateral .From a point out side of the circle the two tangents to the circle are equal. AP = AS,BP = BQ , CR = CQ , and DR = DS Adding AP + BP + CR + DR = AS + BQ + CQ + DS AB + CD = AD + BC 6 + 4 = AD + 7 AD = 3 cm .

Sol :
Let P,Q,R,S be the points where the circle touches the quadrilateral .From a point out side of the circle the two tangents to the circle are equal.
AP = AS,BP = BQ , CR = CQ , and DR = DS
Adding AP + BP + CR + DR = AS + BQ + CQ + DS
AB + CD = AD + BC
6 + 4 = AD + 7
AD = 3 cm .