Tangent — Geometry, what it means and where it is taught
A line touching the circle at exactly one point.
Taught in Geometry.
Where it is taught
Practise this idea
4 questions in the course bank use Tangent, in Circle Angles, Arcs & Chords.
Problem 1
A tangent touches a circle of radius 9 at T. From P, OP = 15. Find PT.
Worked answer
12
PT2 = 152 - 92 = 144
PT = 12
Problem 2
A tangent meets the radius at the point of contact at
- 90°
- 45°
- 180°
- any angle
Worked answer
90°
A tangent is perpendicular to the radius there.
Problem 3
Two tangents from an external point cut arcs of 210° and 150°. Find the angle at the point.
Worked answer
30
210 - 150 = 60
60 ÷ 2 = 30°
Problem 4
Two tangents are drawn from an external point. One has length 3x + 2, the other 5x - 8. Find x.
Worked answer
5
3x + 2 = 5x - 8
10 = 2x
x = 5