2022 · Q98
ABCD is a trapezium in which AB is parallel to DC. The vertices A, B, C and D pass through a circle. Which of the following are correct?1. AD = BC2. ∠A + ∠C = 180°3. ∠A + ∠D = 180°Select the correct answer using the code given below :
Elementary MathematicsQuadrilaterals and Polygons
- AOnly 1 and 2
- BOnly 2 and 3
- COnly 1 and 3
- D1, 2 and 3
Explanation
A cyclic trapezium must be isosceles, so AD = BC (1 true); cyclic gives ∠A+∠C = 180° (2 true); AB∥DC gives consecutive interior angles ∠A+∠D = 180° (3 true). All three are independent consequences: isosceles from cyclic+parallel, the opposite-angle sum from cyclic, the consecutive-angle sum from parallel lines. The keyed option is D.