Question

Given circle O with chords CD = 12 and

AB = 12. Perpendiculars are drawn from 0 to

E and to F. The radius of the circle is 10. Find

FB

OE.

Answer 1

• FB=6 Units
• OE= 8 Units

Explanation:

Theorem: A line drawn from the center perpendicular to the chord bisects the chord.

By the Theorem above, Point E and F bisects CD and AB into 6 Units each as seen in the diagram.

Therefore:

|FB|=6 Units

In Right Triangle OED, applying Pythagoras Theorem

`10^2=6^2+|OE|^2\\|OE|^2=100-36\\|OE|^2=64\\|OE|^2=8^2\\|OE|=8 \:Units`

Therefore:

• FB=6 Units
• OE= 8 Units