Question

A chord of length 10 cm is at a distance of 12 cm from the center of a circle. Find the radius of the circle.

Answer 1

Answer:

8 cm

Step-by-step explanation:

Radius = √10²-(12/2)²

Radius= √100-36

Radius= √64

Radius= 8cm

Answer 2

Answer:

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The distance of the chord from the circle is 8 cm.

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Step-by-step explanation:

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Let AB=12 cm be the chord of the circle with radius AO=10 cm

Draw OP⊥AB  Join OA

AP=  2 1  AB=  2 1 ×12=6cm

In △APO,∠P=90

∴ $AO^{2}$ =  $AP^{2}$ +  $OP^{2}$

⇒ $10^{2}$  = $6^{2}$ +  $OP^{2}$

⇒ $OP^{2}$  = 100 − 36

⇒  $OP^{2}$ = 64

⇒ OP = 8cm

Hence the distance of the chord from the circle is 8 cm.

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