Tangent length from an external point

A circle has radius 3 cm. A point is 5 cm from the centre. Find the length of the tangent from that point.

Step-by-step

1. 5² − 3² = 25 − 9 = 16
   The radius is perpendicular to the tangent, forming a right triangle
2. √16 = 4
   Tangent length = √(centre distance² − radius²)

Why it works

A tangent is perpendicular to the radius at the touch point, so the radius, the tangent and the line to the centre form a right triangle: tangent = √(d² − r²).

Common mistakes

• Subtracting radii instead of using Pythagoras.
• Answering with the distance to the centre instead of the tangent length.

Related

parabola-vertex similar-triangle-3-4-5-shortest-6 tangent-length-radius-8-distance-17