Tangent length: radius 6 cm, distance 10 cm

A circle has a radius of 6 cm. A point outside the circle is 10 cm from the centre. Find the length of the tangent from that point to the circle.

Step-by-step

1. 10² − 6² = 100 − 36 = 64
   The radius is perpendicular to the tangent, forming a right triangle
2. √64 = 8
   Tangent length = √(centre distance² − radius²)

Why it works

A tangent is perpendicular to the radius at the point of contact, so the radius, the tangent and the line from the centre to the outside point form a right triangle and the tangent length follows from Pythagoras.

Common mistakes

• Subtracting the radius from the distance: 10 − 6 = 4.
• Adding the two squares before taking the square root instead of subtracting them.

Related

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