SAT Math: Identify properties of a tangent line to a circle
15+ practice questions in Praczo
The concept, explained
- 1
A tangent line touches a circle at exactly one point — the point of tangency.
- 2
A tangent line is ALWAYS perpendicular to the radius drawn to the point of tangency. This is the key fact most tangent-line SAT problems test.
- 3
Two tangent segments drawn to a circle from the same external point are equal in length.
- 4
When a problem gives a tangent line and a radius at the point of tangency, you almost always have a right triangle — perfect for Pythagorean theorem or trig.
- 5
The distance from the center of a circle to any tangent line equals the radius.
- ✗ Forgetting that the tangent–radius angle is exactly 90° and using some other angle instead.
- ✗ Mistaking a secant (which intersects the circle at two points) for a tangent (one point).
- ✗ Using the diameter instead of the radius when setting up the right triangle.
SAT-style practice
A line is tangent to a circle at point P. The radius to point P has length 5, and the distance from the center of the circle to an external point Q on the tangent line is 13. What is the distance from P to Q along the tangent line?
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