Question

find the length the chord which is at a distance of 8cm from the centre of circle of diameter 34cm

Answer 1

Answer:

Step-by-step explanation:

Given AD is the diameter of the circle of length is AD = 34 cm

and AB is the chord of the circle of length is AB = 30 cm

The distance of the chord from the center is OM

Since the line through the center to the chord of the circle is the perpendicular bisector, we have

∠OMA = 90° and AM = BM

So, ΔAMC is a right triangle.

From Pythagorean Theorem

OA2 = AM2 + OM2 ...............1

Since the diameter AD = 34 cm

So, theradius of the circle = 34/2 = 17 cm

Thus, OA = 17 cm

Since AM = BM and AB = 30 cm, we have AM = BM = 15 cm

Substitute the values in equation 1, we get

    OA2 = AM2 + OM2

=> 172 = 152 + OM2

=> OM2 = 289 – 225

=> OM2 = 64

=> OM = √64

=> OM = 8

So, the distance of the chord from the center is 8 cm