Multiple choice

If chord PQ of a circle have length equal to the radius then the distance of chord from centre in terms of radius is

  1. $\displaystyle \frac{\sqrt{3}}{4} r$
  2. $\displaystyle \frac{\sqrt{5}}{2} r$
  3. $ \frac { 3\sqrt { 3 } }{ 2 } r $
  4. $\displaystyle \frac{\sqrt{3}}{2} r$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the chord length equals the radius, it forms an equilateral triangle with the two radii connecting the center to the chord endpoints. The distance from the center to the chord is the altitude of this equilateral triangle, which is calculated as r * sin(60 degrees) = r * sqrt(3)/2.

AI explanation

When a chord length equals the radius r, the triangle formed by the two radii and the chord is equilateral. The perpendicular distance from the centre to the chord acts as the altitude of this equilateral triangle, splitting it into two 30-60-90 right triangles. Using the properties of a 30-60-90 triangle, this altitude is calculated as r * sin(60 degrees), which equals sqrt(3)/2 * r.

Keep practicing — related questions