Question

2. A chord of length 8 cm is drawn at a distance
of 3 cm from the centre of a circle. Calculate
the radius of the circle.​

Answer 1

Step-by-step explanation:

Let AB be the chord of the circle

O be the centre of the circle

OP is the line perpendicular to the chord

OP=3 cm ,AB= 8 cm

Perpendicular drawn from the centre of the circle to the chord bisects the chord

AP=PB=1/2AB

=1/2×8 = 4

join OA

OA is the radius of the circle

By Pythagoras theorem

(OA)2=(OP)2+(AP)2

=(3)2+(4)2

=9+16

OA =√25 = 5

The radius of the circle is 5cm

Answer 2

Answer:

Radius = 5cm

Step-by-step explanation:

Let the center be O

Let the chord be AB = 8cm

Let the distance between the center and chord be OP = 3cm

Radius bisects the chord.

So, AP = PB = 1/2 of 8 = 4cm

In AOP, OPA = 90°-------(Radius is perpendicular to the chord)

OP² + AP² = AO²------(pythagoras theorem)

3² + 4² = AO²

9 + 16 = AO²

√25 = AO

5cm = AO

Therefore, the radius of the circle is 5cm.

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