Tangent Lines and Chord Properties — Practice Set

A line is tangent to a circle at point $P$. A radius is drawn to point $P$. What angle do the tangent line and radius form?

A right triangle has a hypotenuse of $10$ and one leg of $6$. Find the length of the other leg.

Which statement correctly describes a chord of a circle?

A circle has center $O$ and radius $5$. A tangent line touches the circle at point $P$. If the distance from $O$ to a point $Q$ on the tangent line is $13$, find $PQ$.

A circle has radius $7$. A tangent line from external point $P$ touches the circle at $T$. The distance $OP = 25$. Find the length of the tangent segment $PT$.

Two tangent lines are drawn from external point $P$ to a circle of radius $6$. The distance from $P$ to the center $O$ is $10$. Find the length of each tangent segment.

A circle has radius $10$ and a chord is $8$ units from the center (perpendicular distance). Find the chord length.

Two chords intersect inside a circle. One chord is divided into segments of $6$ and $4$. The other chord is divided into segments of $3$ and $x$. Find $x$.