Question

Let a circle has a radius of $5$ cm and $XY$ be its chord of length $6$ cm.Find the distance of the chord from the center of the circle? (in cm)

• A. $3$
• B. $4$
• C. $5$
• D. $7$

Answer 1

The correct option is B $4$

We know that, the perpendicular from the center of a circle to a chord bisects the chord.

$\therefore XZ=3(\because OZ\perp XY)$
Using pythagorean theorem in $△OXZ$
$O{Z}^2+Z{X}^2=O{X}^2\Rightarrow O{Z}^2+3^2=5^2\Rightarrow O{Z}^2=16\Rightarrow OZ=4$
Hence, the distance of the chord from the center of the circle is $4$ cm.