Question

If two chords of a circle are equidistant from the center of the circle then they are

• A. Equal to each other
• B. Not equal to each other
• C. Intersect each other
• D. None of these

Answer 1

The correct option is A Equal to each other

Let $AB,PQ$ be two chords, $OC$ and $OR$ be their distance from center.

Given

$OC=OR$

We know that $BC=AC$ and $PR=SR$ because perpendicular line from center bisects the chord.

In $△OBC$

$B{C}^2=r^2–O{C}^2–\left(1\right)$

In $△OPR$

$O{P}^2=R{P}^2+O{R}^2$

$P{R}^2=r^2–O{C}^2–\left(2\right)$

$\left(1\right)=\left(2\right)$

$⟹BC=PR⟹2BC=2PR$

$AB=PQ$