Circles • Topic 7 of 7

Tangents

A tangent is a line that touches a circle at exactly one point, called the point of tangency. Its defining property is that a tangent is perpendicular to the radius drawn to the point of contact — they meet at 90°. This right angle lets you use the Pythagorean theorem in problems involving a tangent and a radius. Two tangent segments drawn to a circle from the same external point are equal in length. Compare a tangent (one point) with a secant (two points) and a chord (segment inside). The SAT mainly tests the perpendicular-to-the-radius property and the equal-tangents fact.

A circle with a tangent line touching at point P and the radius meeting it at a right angleTangentsPrTangent ⊥ radius at the point of contact.

✅ Solved examples

1. A line touching a circle at exactly one point is a:
A tangent.
2. A tangent meets the radius at the point of contact at what angle?
90° (it is perpendicular).
3. Two tangent segments from the same external point are:
Equal in length.
4. How many points does a tangent share with the circle?
One.

✏️ Practice — try these, take hints as needed

1. A line touching a circle at one point is called a:
One contact point.
—
—
Tangent.
2. A tangent is ___ to the radius at the point of contact.
They meet at 90°.
—
—
Perpendicular.
3. Two tangents from the same outside point have what relationship?
Equal-tangents property.
—
—
Equal lengths.
4. How many points does a tangent line share with the circle?
Just touches.
—
—
One.
5. A line crossing a circle at two points is a secant, but one touching at one point is a:
Single touch.
—
—
Tangent.

📝 Topic test — 8 questions

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