2022 · Q99
ABCD is a cyclic quadrilateral. AB and DC when produced, meet in E. Which of the following statements is/are correct?1. ΔEBC is similar to ΔEAD.2. ∠ CBE + ∠ DAE = 180°.Select the correct answer using the code given below :
Elementary MathematicsQuadrilaterals and Polygons
- AOnly 1
- BOnly 2
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
∠E is common and ∠EBC = 180°−∠ABC = ∠ADC = ∠ADE, so ΔEBC ∼ ΔEAD (statement 1 true). But ∠CBE+∠DAE = 360°−(∠ABC+∠BAD), which is not 180° in general (statement 2 false). Only statement 1 is correct. The keyed option is A.