Question

If the distance between center to chord is 12 cm and the length of the chord is 10 cm, then the diameter of the circle is

• A. 26 cm
• B. 14 cm
• C. 13 cm
• D. 30 cm

Answer 1

Answer:

A. 26 cm

Given:

Given a circle with a chord of length = 10 cm = AB

Distance between centre to chord = 12 cm = OP

Concept:

The line perpendicular from the center to the chord bisects the chord.

Calculations:

From ΔAPO right-angled at P, Using Pythagoras theorem

AO² = AP² + OP²

AO² =  5² + 12²

⇒ AO = 13 cm = radius of the circle

The diameter of the circle = AO + OZ = 13 + 13 = 26 cm