The question on the image seems to be related to a circle with a chord $PQ$ and a radius $OR$ perpendicular to the chord. The problem states:

• $OR$ is the perpendicular from the center $O$ to the chord $PQ$, and its length is $8 \, \text{cm}$.
• The radius of the circle is $10 \, \text{cm}$.

You are asked to find the length of the chord $PQ$.

Solution:

This is a typical geometry problem involving a circle, a radius, and a perpendicular from the center to a chord. When a radius is drawn perpendicular to a chord, it bisects the chord. Therefore, $OR$ is the perpendicular distance from the center $O$ to the chord, and the length of $PQ$ can be found using the Pythagorean theorem.

Let:

• $O$ be the center of the circle,
• $OR = 8 \, \text{cm}$,
• The radius $OQ = 10 \, \text{cm}$ (since $OQ$ is a radius of the circle),
• $P$ and $Q$ are the points where the chord intersects the circle.

Now, let $PR$ be half the length of the chord ( PQ \