A chord of a circle has a length of 16 cm. The angle subtended by the chord at a point on the circumference is 45°. What is the distance from the center of the circle to the chord?

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Accepted Answer

1. The inscribed angle is $45^\circ$, so the central angle is $90^\circ$.  
2. Use the chord formula: $16=2R\sin(90^\circ/2)=2R\sin45^\circ=R\sqrt{2}$. So $R=8\sqrt{2}$.  
3. The distance from centre to chord is $R\cos45^\circ$. So it is $8\sqrt{2}\cdot\dfrac{\sqrt{2}}{2}=8$.  
4. The distance is 8 cm. **Answer: (c)**

FINAL_ANSWER: c

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