If distance between centre to chord is 12 cm and length of chord is 10 cm,…

The perpendicular drawn from the centre of a circle to a chord always bisects that chord. This perpendicular, half the chord, and the radius therefore form a right-angled triangle, so radius2 = (perpendicular distance)2 + (half-chord)2 by the Pythagorean theorem.

1. Half of the chord = 10 cm divided by 2 = 5 cm, since the perpendicular from the centre bisects the chord.

2. The perpendicular distance (12 cm) and the half-chord (5 cm) are the two legs of a right triangle whose hypotenuse is the radius, so radius2 = 122 + 52.

3. radius2 = 144 + 25 = 169, so radius = the square root of 169 = 13 cm.

4. Diameter = 2 times radius = 2 times 13 = 26 cm.

Checking: 132 = 169 = 122 + 52, confirming the right triangle relationship holds, so the diameter is 26 cm.

Therefore, the diameter of the circle is 26 cm.