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Lesson 3 J.Byrne 2012

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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

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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

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

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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

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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

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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

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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

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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

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