Tangent length: radius 8 cm, distance 17 cm

A circle has a radius of 8 cm. A point outside the circle is 17 cm from the centre. Find the length of the tangent from that point to the circle.

Step-by-step

1. 17² − 8² = 289 − 64 = 225
   The radius is perpendicular to the tangent, forming a right triangle
2. √225 = 15
   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: 17 − 8 = 9.
• Adding the two squares before taking the square root instead of subtracting them.

Related

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