Multiple choice

A chord of length 42 cm is drawn in a circle having diameter 58 cm. What is the minimum distance of other parallel chord of length 40 cm in the same circle from 42 cm long chord?

  1. 4 cm

  2. 1 cm

  3. 3 cm

  4. 2 cm

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For chord length L in a circle of radius R, the perpendicular distance from center to chord is sqrt(R² - (L/2)²). For 42 cm chord: d1 = sqrt(29² - 21²) = sqrt(841 - 441) = sqrt(400) = 20 cm. For 40 cm chord: d2 = sqrt(29² - 20²) = sqrt(841 - 400) = sqrt(441) = 21 cm. The chords are parallel and on opposite sides of the center (since the question asks for minimum distance). Minimum separation = 20 + 21 = 41 cm. But wait - the answer options are small (1-4 cm), suggesting these chords are on the SAME side of center. Then minimum distance between them = |21 - 20| = 1 cm. Answer is 1 cm (Option B).