Lesson 3 J.Byrne 2012

Tangent A line touches a circle at one point on the circumference. It is called a Tangent. The point of contact is called the POC. The line going from the centre of the circle to the Tangent is called the Normal. The Tangent is always at 90° to the Normal J.Byrne 2012

Tangent to a Point Draw a tangent from a circle to a point. Draw a line from the point to the centre of the circle. Bisect the line and draw a semicircle from the midpoint. J.Byrne 2012

Tangent to a Point Draw a tangent from a circle to a point. J.Byrne 2012

Tangent to a Point At the point where the semicircle cuts the circle draw a normal back to the centre of the circle. Tangent is always at 90° to the Normal J.Byrne 2012

Exterior Tangent to two circles Draw circles and join centres. Draw semicircle Subtract the radius of the smaller circle from the larger circle. 56 – 34 = 22 Draw a circle with a radius of 22 from the centre of the larger circle J.Byrne 2012

Exterior Tangent to two circles Draw a normal where the new circle and the semicircle intersect. POC This gives a line parallel to the required tangent through centre of other circle Then draw a parallel normal in other circle R34 Draw a tangent through both points of contact J.Byrne 2012

Interior Tangent to two circles Draw circles and join centres. Draw semicircle Add the radius of the smaller circle to the radius of the larger circle = 90 Swing an arc of 90 from the centre of the larger circle J.Byrne 2012

Interior Tangent to two circles Draw a normal where the new circle and the semicircle intersect. Then draw a parallel normal in other circle R34 Draw a tangent through both points of contact J.Byrne 2012