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

To determine the length of OM, we first need to calculate the diameter of the circle.

The diameter is given by the sum of the lengths of AP and PB: $Diameter = AP + PB = 16 ext{ m} + 4 ext{ m} = 20 ext{ m}$

So, $OM = \frac{Diameter}{2} = \frac{20}{2} = 10 ext{ m}$

To find the length of MP, we can use the Pythagorean theorem since triangle OPM is a right triangle.

Given:

• OP = 10 m (length from center to midpoint of chord)
• OM is perpendicular to MN, hence $ $OM^2 = OP^2 + MP^2$ Substituting known values: $10^2 = 6^2 + MP^2$ $100 = 36 + MP^2$ $MP^2 = 100 - 36$ $MP^2 = 64$ Taking the square root: $MP = 8 ext{ m}$