Question

Find the length of the chord which is at a distance of 9cm from the centre of the circle of radius 15cm.

Answer 1

R = hypotenuse
Distance= perpendicular
1/2 chord = base
chord×1/2 = 15²-9²
chord = {√( 225 -81)}×2
chord= (√ 144 )×2
chord= 12×2
chord =24 cm

Answer 2

Given:

• The radius of the circle = 15 cm
• Distance from the centre = 9 cm

To Find:

• The length of the chord.

Solution:

Let us first construct a figure using the given data for clear calculations.

From the figure, we get to know that we should find the length of the chord AB.
Consider ΔOAC,

We are applying the Pythagoras theorem for ΔOAC.

⇒ $OA^2=AC^2+OC^2$

On substituting the values given in the above equation we get,

⇒ $15^2=AC^2+9^2$

⇒ 225 = $AC^2$ + 81

On rearranging the etrms in terms of AC in the above equation we get,

⇒ AC = √(225-81) {subtracting the terms}

⇒ AC = √144

⇒ AC = 12 cm

The length of the chord AB = 2(AC) = 2(12) = 24 cm

∴ The length of the chord = 24 cm