Question

A chord is 15 cm long. It is 9 cm from the center of the circle. What is the radius of the circle?

Answer 1

Answer:

11.72cm

Step-by-step explanation:

Given a chord of distance of 15cm, if it is 9cm from the center of a circle, this means that the 9cm length will be projecting from the centre of the circle perpendicular to the chord and passing through its centre.

Since the radius of a circle is a line that is drawn from the centre of a circle to ts circumference, the set up will form a right angles triangle within the circle with the hypotenuse as the radius and the other two sides as the opposite and adjacent respectively. Using the Pythagoras theorem to get the length of the radius (hypotenuse);

hyp² = opp² + adj²

Let the opposite be the 9cm length

Adjacent will be half of the chord length = 15/2 = 7.5cm

Substituting this values into the formula we will have;

hyp² = 9² + 7.5²

hyp² = 81+56.25

hyp² = 137.25

hyp² = √137.25

hyp = 11.72

Hence the radius of the circle is approximately 11.72 cm long