Question

In a circle with centre O, $OD\perp chordAB$. If BC is the diameter, then

• A. $AC=BC$
• B. $OD=BD$
• C. $AC=2OD$
• D. none of these

Answer 1

The correct option is C $AC=2OD$

Given: $OD$ is perpendicular to chord $AB$ of a circle where centre is $O$. $BC$ is a diameter of the circle.

therefore $OD\perp AB$ and $D$ is the mid-point of $AB$

The perpendicular drawn from the centre of a circle to a chord bisects the chord.

In triangle $BAC$,

$D$ is the mid-point of $AB$ and $O$ is the midpoint of $BC$

$OD$ parallel to $AC$ ( By Basic Proportionality theorem)

and $OD=\frac{1}{2}AC$

$AC=2OD$

option C is the answer.