Problem: In a circle of radius 5 units, CD and AB are perpendicular diameters. A chord CH cutting AB at K is 8 units long. The diameter AB is divided into two segments whose dimensions are:
Answer Choices:
A. 1.25,8.75
B. 2.75,7.25
C. 2,8
D. 4,6
E. none of these
Solution:
Let KB=x and CK=y. Then y(8−y)=x(10−x) and y2=(5−x)2+52.∴8y−y2=50−y2;∴y=25/4.
∴x=210−(15/2)=45 and 10−x=435
so that (A) is the correct choice.