A line that touches a circle at one point. The tangent is perpendicular to the radius, two tangents from a point are equal, and problems about circles inside triangles and quadrilaterals.
3 lessons, about 1 h 20 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabA line that touches a circle at exactly one point is a tangent. The key fact is that a tangent is at right angles to the radius drawn to the point where it touches. From this one theorem we can find lengths and angles that look hard at first.
From a point outside a circle, two tangents can be drawn, and they have the same length. The centre lies on the line that bisects the angle between them. With Pythagoras we find the length of a tangent, and with angles of a four-sided figure we find the angle between two tangents.
A circle drawn inside a triangle or a four-sided figure touches every side. The equal-tangent theorem then gives a handful of neat rules: the tangent lengths from each corner of a triangle, the radius of the circle inside a right triangle, and the sums of opposite sides of a four-sided figure.
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