Question

A circle has a circumference of $20\pi$ units. One of its chord $PQ$ has a length of $12$ units. If $OR\perp PQ,$ then which of the following option is incorrect?

• A. radius of the circle is $10$ units
• B. $OP=OQ$
• C. $PR=6$ units
• D. $RQ=5$ units

Answer 1

The correct option is D $RQ=5$ units

Given, circumference $=20\pi$
$\Rightarrow 2\pi r=20\pi \Rightarrow r=10$
$\Rightarrow OP=OQ$ (radii)

Given $OR\perp PQ$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> The perpendicular from the centre of a circle to a chord bisects the chord
$\therefore PR=RQ=\frac{PQ}{2}=\frac{12}{2}=6$ units