Question

I’m the circle be, CE equals 13.5. Find BD. Round to the nearest hundredth

Answer 1

Given:

CE = 13.5

AB = 8

To find:

The length of BD.

Solution:

AB and BF are radius of the circle.

BF = 8

Radius BF is perpendicular to the chord CE.

Therefore it BF bisects the chord.

CD = $\frac{1}{2} (13.5)=6.75$

Draw radius BC to complete right triangle BCD.

BC = 8 units

Using Pythagorean Theorem:

$B D^{2}+C D^{2}=B C^{2}$

$B D^{2}+6.75^{2}=8^{2}$

$B D^{2}+45.5625=64$

Subtract 45.5625 from both sides.

$B D^{2}=18.4375$

Taking square root on both sides, we get

$B D \approx 4.29$

The length of BD is 4.29 units.