AI generatedAlgebraGCSE Higher

Equation of a tangent to a circle

Use a radius gradient and perpendicularity.

  • Join the centre to the given point to find the radius gradient.
  • The tangent is perpendicular to that radius.
  • Use the tangent gradient and contact point to find its line equation.

Example 1

Find the tangent to at .

Coordinate graph−6−4−2246−6−4−22460P
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.

Example 2

Find the tangent to at .

Coordinate graph−10−5510−10−55100P
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.

Your turn

Question 1

Find the tangent to at .

Coordinate graph−15−10−551015−15−10−5510150P
Check answer
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.
Question 2

Find the tangent to at .

Coordinate graph−20−15−10−55101520−20−1010200P
Check answer
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.
Question 3

Find the tangent to at .

Coordinate graph−20−101020−20−1010200P
Check answer
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.
Question 4

Find the tangent to at .

Coordinate graph−30−20−10102030−30−20−101020300P
Check answer
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.
Question 5

Find the tangent to at .

Coordinate graph−30−20−10102030−30−20−101020300P
Check answer
Find the gradient from the centre to P.A tangent is perpendicular to the radius at the contact point.Substitute P into .Use the gradient and intercept in the line equation.
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