Question

In the circle below, chord AB passes through the center of circle 0. If the radius OC is perpendicular to chord AB and has length of 7 centimeters,

what is the length of chord BC, to the nearest tenth of a centimeter?
A. 5.3
B. 7.0
C. 9.9
D. 12.1
E. 14.0

Answer 1

Option (C)

Explanation:

In the given circle, AB is a chord passing through the center O.

Therefore,chord AB is a diameter of the circle and OC is the radius.

AO = OB = OC

OC⊥AB, and length of OC = 7 cm

By applying Pythagoras theorem in right ΔBOC,

BC² = OC² + OB²

BC =
`\sqrt{OC^(2)+OB^(2)}`

=
`√(7^2+7^2)`

=
`7√(2)`

≈ 9.9 units

Therefore, Option (C) will be the answer.