CAT 2019 Slot 1 — QA Question 7
Basics of CirclesEasy
In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
Answer & solution
0.5
- B
2.5
- C
3.5
- D
1.5
Solution
The circle can be drawn as shown below. Diameter of the circle = 2 × 11 = 22 cm.
CE = 7, so ED = CD − CE = 22 − 7 = 15.
Let AE be x units, so EB = AB − AE = 20.5 − x.
Using the intersecting chords theorem; AE × EB = CE × ED.
∴ x(20.5 − x) = 7 × 15
Solving this equation, we get x = 10.5, 10.
So, if (AE, BE) = (10.5, 10) or (10,10.5)
Required difference = |BE − AE| = |10.5− 10| = 0.5.
Hence, option (a).