Question

If length of chord of circle is 9 cm and radius is 5 cm then find distance of chord from centre of circle.​

Answer 1

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Answer 2

Let AB = 9 cm. be the chord of the circle with radius AO = 5 cm

• Draw OP ⊥ AB . Join OA

According to the theorem

AP =  1/2 × AB

⇒ AP =  1/2 × 9 cm

⇒ AP = 9/2 cm

⇒ AP = 4.5 cm

• In △APO , ∠A=90°

⇒ (AO)² = (AP)² + (OP)²

⇒ OP = $\sf{\sqrt{(\sf{AO})^{2}-(\sf{AP})^{2}}}$

⇒ OP = $\sf{\sqrt{(\sf{5})^{2}-(\sf{4.5})^{2}}}$

⇒ OP = $\sf{\sqrt{25-20.25}}$

⇒ OP = $\sf{\sqrt{4.75}}$

⇒ OP = 2.179 cm