Tangents to Circles (Cambridge (CIE) IGCSE Additional Maths): Revision Note

Tangents to circles

What is a tangent to a circle?

• A tangent (to a circle) is a line that touches the circle at a single point but does not cut across the circle

  

• A tangent to a circle is perpendicular to the radius of the circle at the point of intersection

How can I find the equation of the tangent line to a circle at a given point?

• STEP 1 Find the gradient of the radius OP

• STEP 2 Find the gradient of the tangent As they are perpendicular, if the gradient of the radius is $m_r$, then, the gradient of the tangent is $m_t=-\frac{1}{m_r}$ (Negative reciprocal) Alternatively,

• STEP 3 The equation of the tangent is the equation of the line with that gradient that goes through point P (x₂, y₂) Write down the equation using $y-y_2=m_t\left(x-x_2\right)$where $m_t$is the gradient