The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the center.

Step 1: Construct a imaginary figure according to given hints
EXAMPLE: Let PQ be a chord of a circle with centre O and radius 13cm
such that PQ = 24cm.
Step 2: Draw (OM) perpendicular line to the chord (PQ) and join the center and the end point of the chord.
Step 3: Find the base of the right angle triangle
NOTE: The perpendicular from the centre of a circle to a chord bisects the chord.
EXAMPLE ∴ Base PM = 12cm
Step 4: Recall the Pythagoras theorem to calculate the unknown value
NOTE: (Hypotenuse)^2 = (height)^2 + (Base)^2
Step 5: Substitute all the known values in the Pythagoras formula and simplify the equation.
EXAMPLE: In △OMP, we have
OP2 = OM2 + PM2
⇒ 132 = OM2 + 122
⇒ OM = 5cm.
Hence, the distance of the chord from the centre is 5cm.