If $AB$ and $AC$ are two chords of a circle of radius $5$ cm such that $AB = AC = 4\sqrt 5$ cm, then the length of the chord $BC$ is

Drawing the radius to point A and dropping a perpendicular to the midpoint of BC creates a kite shape with the two equal chords, where the radius bisects angle BAC. Using the right triangle formed, the cosine of half of angle BAC is the adjacent side (half of AB) over the radius, which is 2 times the square root of 5 divided by 5. The perpendicular distance from the center to chord BC is the radius times the sine of this half-angle, which calculates to the square root of 5. Applying the chord length formula, BC is 2 times the square root of (5^2 minus (square root of 5)^2), resulting in 2 times the square root of 20, which simplifies to 8 cm.

• Thanks
• Wrong explanation