Circles: tangents
Tangents meet the radius at 90°, and two tangents from a point are equal.
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A tangent just touches a circle, and it meets the radius at 90°.
Look: The radius meets the tangent at a right angle.
✏️ Your turn!
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1Point 10 cm from centre, radius 6 cm. Tangent?
2Tangents from a point inside the circle?
3Two tangents from one point: equal?
! Careful!
✗Thinking the angle depends on the circle.
✓It is always 90°.
✗Using 13 as a short side.
✓Centre to outside point is the longest side.
See the whole lesson on one page
A tangent just touches a circle, and it meets the radius at 90°.
From a point outside, you can draw two tangents, and they are the same length. Use the right angle and Pythagoras.
Think of it like thisA bicycle wheel touches the road at one point. The spoke to that point stands straight up from the road.
Solved together
A point is 13 cm from the centre of a circle with radius 5 cm. How long is the tangent from it?
The radius and tangent make a right angle, so draw a right triangle. 13 cm is the longest side.
Pythagoras.
tangent² = 13² − 5² = 169 − 25 = 144tangent = 12
AnswerThe tangent is 12 cm.
Now practise it
Kanakku makes new questions on circles: tangents every time. It shows the working and gives a hint when you are stuck.