Multiple choice

There is a circle which has a diameter PQ = 34 cm. A chord which is equal to 16 cm, has been drawn from point P to point Y. Find the least distance between centre of circle and the chord of circle.

  1. 15 cm

  2. 16 cm

  3. 17 cm

  4. 18 cm

  5. 19 cm
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A Correct answer
Explanation

The radius of the circle is 34/2 = 17 cm. A chord of 16 cm is drawn. The distance from the center to the chord is the perpendicular bisector, forming a right triangle with the radius as the hypotenuse (17) and half the chord as one leg (8). By Pythagorean theorem, distance^2 + 8^2 = 17^2, so distance^2 = 289 - 64 = 225, distance = 15 cm.

AI explanation

The radius of the circle is half of the diameter, so the radius is 34 divided by 2, which is 17 cm. Using the property that the perpendicular from the center to a chord bisects the chord, we apply the Pythagorean theorem to the right triangle formed by the radius, half the chord, and the perpendicular distance. Half of the 16 cm chord is 8 cm, so the distance equals the square root of (17 squared minus 8 squared). This calculates to the square root of 225, which is 15 cm.

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