2016 · Q70
ABCDA is a con-cyclic quadrilateral of a circle ABCD with radius r and centre at O. If AB is the diameter and CD is parallel and half of AB and if the circle completes one rotation about the centre O, then the locus of the middle point of CD is a circle of radius
Elementary MathematicsCircles
- A3r/2
- B2r/3
- C{23r}3
- D{3r}2
Explanation
CD is parallel to the diameter AB and half its length, so CD = r. The midpoint M is at distance √(r²−(r/2)²) = √3·r/2 from the centre O. As the circle rotates about O, M traces a circle of radius √3·r/2 — option D (rendered '{3r}2').