Multiple choice

A chord of length $16$ cm is drawn in a circle at a distance of $15$ cm from its center. Find the radius of the circle.

  1. $12$ cm
  2. $15$ cm
  3. $17$ cm
  4. $34$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This creates a right triangle with legs 8 cm (half of 16) and 15 cm. The hypotenuse (radius) is sqrt(8^2 + 15^2) = sqrt(64 + 225) = sqrt(289) = 17 cm.

AI explanation

A line from the center perpendicular to a chord bisects the chord, forming a right triangle with a leg of 8 cm (half the chord) and another leg of 15 cm (the distance from the center). By the Pythagorean theorem, the radius is the square root of (8^2 + 15^2). Calculating this gives the square root of (64 + 225), which is the square root of 289, making the radius 17 cm.

Keep practicing — related questions