Complete the following theorem statement: The line drawn from the centre of a circle to the midpoint of a chord is … The diagram below shows a circle with centre O - NSC Technical Mathematics - Question 7 - 2022 - Paper 2

We apply the theorem that states the line drawn from the centre of a circle to the midpoint of a chord is perpendicular to the chord. Therefore, we can use the Pythagorean theorem to solve for MP:

• We know OP is perpendicular to MN, which implies (OP = 90^{\circ}).

Using the Pythagorean theorem:

$OM^2 = OP^2 + MP^2$

Substituting the known values:

$10^2 = 6^2 + MP^2$

Calculating:

$100 = 36 + MP^2$

Subtracting 36 from both sides yields:

$MP^2 = 64$

Taking the square root gives:

$MP = 8 ext{ m}$