find the distance from the centre of the circle of a chord 16cm long, if the radius of the circle is 12cm.?

VTPETERS2002

5 years ago

Picture a line from the middle of the 16cm chord to the center of the circle — i.e. the perpendicular bisector of the chord; that is the distance we need to find.

If we connect one end of the chord to the center the circle (with a radius of 10cm) that is the hypotenuse of a right triangle, where one side is 8cm (to the middle of the chord) and the third side is the unknown distance, X.

At this point, we may use the Pythagorean Theorem to determine the length of the third side: X^2 + 8^2 = 10^2.

However, it’s much easier to note that 6–8–10 is a Pythagorean Triple (or just double each side of the Pythagorean Triple 3–4–5 ), so the distance is 6cm.

Jerrycurl12

5 years ago

given r=12cm

length of a chord=16cm

let the distance from the center of the circle be x

using pythagoras theorem

12²=x²+8²

144=x²+64

144-64=x²

x=√80

=8.9cm