Question

AB is a chord of a circle at a distance 5 cm from the centre. If the length of the chord is 24 cm then the radius is ?​

Answer 1

Answer:

13 cm

Step-by-step explanation:

Draw a perpendicular from center O on the chord. Suppose that perpendicular intersects AB( chord ) at C.

Then, join the center and A, again with another line join center and B.

Now, two triangles are formed.

In ∆AOC and ∆BOC,

• AO = BO ( radius )

• OC = OC ( common )

• /_ OCA = /_ OCB = 90°

Hence both the triangles are congruent.

Now it can be said AC = BC

It means that perpendicular divides the chord in two equal parts.

Length of each part = 1/2 of chord = 1/2 of 24 cm = 12 cm

So, AC = 12 cm

Distance between center and chord = OC = 5 cm

In ∆AOC, OC is at 90°, so we can use Pythagoras theorem,

= > radius² = AC² + OC²

= > AO² = 12² + 5²

= > radius² = 144 + 25 = 169

= > radius = √169 = 13

Radius of circle is 13 cm

Answer 2

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