Problem

Point \(P\) is \(13~\text{units}\) from the center of a circle with radius \(5\). Compare the center distance with the radius, classify \(P\) as inside, on, or outside the circle, and state the number of real tangents from \(P\).

Circle centered at O with radius 5 and point P located 13 units from O; no tangent segments are shown.

Big Picture

What this problem is really about

Before constructing tangents, classify the point by comparing its center-to-point distance directly with the radius. We’ll use that comparison to determine the inside, on-circle, or outside case and then translate the case into the number of real tangent lines.

Answer choices

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Preview only

P is on the circle, so exactly one tangent can be drawn at P.

P is outside the circle, so exactly one tangent can be drawn from P.

P is inside the circle, so no tangents can be drawn from P.

P is outside the circle, so two tangents can be drawn from P.

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Point \(P\) is \(13~\text{units}\) from the center of a circle with radius \(5\). Compare the center distance with the radius, classify \(P\) as inside, on, or outside the circle, and state the number of real tangents from \(P\).

What this problem is really about

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