2016 · Q53
If a quadrilateral has an inscribed circle, then the sum of a pair of opposite sides equals
Elementary MathematicsQuadrilaterals and Polygons
- AHalf the sum of the diagonals
- BSum of the other pair of opposite sides
- CSum of two adjacent sides
- DNone of the above
Explanation
A quadrilateral with an incircle is tangential: from each vertex the two tangent segments to the circle are equal in length. Adding the four pairs of equal tangents shows the sums of each pair of opposite sides are equal. Hence option B; the diagonals play no role.