Question

find the length of a chord which is at a distance of 8 cm from the centre of circle of radius 17 cm

Answer 1

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Answer 2

Given:

The radius of the circle=17cm

Distance of the chord from the centre=8cm

To find:

Length of the chord

Solution:

We can find the radius by following the given process-

From the given information, we know that the radius, perpendicular to the center, and the chord form a right-angled triangle.

Let the length of the chord be 2C cm.

But in the triangle, the base is only half of the chord.

So, the base of the triangle formed= length of chord/2

=2C/2= C cm

Using the Pythagoras theorem, we get

${radius}^{2} = {base}^{2} + {perpendicular}^{2}$

${17}^{2} = {C}^{2} + {8}^{2}$

$289 = {C}^{2} + 64$

${C}^{2} = 289 - 64$

${C}^{2} = 225$

C=√225

C= 15 cm

Length of chord=2C

=2×15

=30cm

Therefore, the length of the chord is 30 cm.