2022 · Q96
ABCD is a parallelogram. A circle through A, B and C intersects CD (produced) at E. Which of the following is/are correct?1. AE = AD2. CD = DESelect 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
With A(0,0), B(b,0), D(d,h), C(b+d,h), the circle through A, B, C meets the line y = h again at x = −d, i.e. E(−d,h). Then AE = √(d²+h²) = AD, so statement 1 holds; but DE = 2d while CD = b, so statement 2 fails in general. Only statement 1 is correct. The keyed option is A.