Question

A chord is 8 in. long. It is 1 in. from the center of the circle. What is the radius of the circle? Round to the nearest tenth.

Answer 1

Answer:

Let radius of the circle be x in.

The line joining any chord of the circle and the centre bisects the chord and is perpendicular to the chord.

So, if the diameter is AB, centre is O, then radius is AO.

Consider the chord CD = 8 in. and its distance from the centre OP = 1 in. Then, CP = 4 in. and OP perpendicular to CD / CP. Join CO, another radius of the circle.

Consider triangle COP. Here, angle CPO = 90°

So, by Pythagoras Theorem, we have

CO² = CP² + OP²

=> x² = 8² + 1²

=> x² = 65

=> x = sqrt(65) = 8.06 (approx upto 2 decimal places)

Hence, radius of the circle is 8.06 in.