Question

In the given figure, AD is a diameter of a circle with centre O and AB is a chord. If AD = 34 cm

and the distance of the chord from the centre is 8cm, find the length of chord AB​

Answer 1

Answer:

diameter of the circle of length is AD = 34 cm

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

Distance of the chord from the centre is OM.

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

∠OMA = 90° and AM = BM.

∴ ΔAMC is a right triangle.

Apply Pythagorean Theorem

OA2 = AM2 + OM2 --------(1)

Since the diameter AD = 34 cm., radius of the circle is 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 = 8. Distance of the chord from the centre is 8 cm.

Step-by-step explanation:

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