Q. 43.6( 10 Votes )
If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.
Given: sides of a quadrilateral touch a circle.
To prove: sum of a pair of opposite sides is equal to the sum of the other pair
Theorem Used: The length of two tangents drawn from an externa point are equal
Let ABCD is a quadrilateral which touches the circle at points P,Q,R and S.
Since length of a tangent drawn from external points to a circle are equal.
DR = DS ----(i)
CR = CQ-----(ii)
AP = AS-----(iii)
BP = BQ-----(iv)
Adding four equation we get,
DC+AB = DA+CB
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