Question

In a circle of radius 5 units CD and AB are perpendicular diameters A of chord CH cutting AB at K is 8 unit long.The diameter AB is divided into two segments whose dirnensions are :

• A. 1.25, 8.75
• B. 2.75, 7.25
• C. 2, 8
• D. 4, 6
• E. none of these

Answer 1

The correct option is A 1.25, 8.75

$CH=kCD=10\therefore HD=\sqrt{100-64}=6$

OCK is similar to HCD.

$\frac{OC}{HC}=\frac{OK}{HD}⟹\frac{5}{8}=\frac{OK}{6}\therefore OK=\frac{15}{4}AK=5-OK,BK=5+OK\therefore AK=1.25,BK=8.75$