Constructing Tangents and Bisecting Lines in Geometry
Construct tangents and bisect lines in geometry, starting from a point outside a circle. Learn the step-by-step process of bisecting lines and creating circles with specific diameters to find points of contact for tangents. Understand the relationship between triangles constructed in semi-circles and the concepts of normal and tangent lines.
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Presentation Transcript
Tangents Tangents A tangent from a given point outside a circle
KEYWORDS KEYWORDS P
KEYWORDS KEYWORDS P Join P to the centre of the circle
KEYWORDS KEYWORDS Bisect Bisect P Bisect the line from the point to the centre
KEYWORDS KEYWORDS Bisect Bisect P Bisect the line from the point to the centre
KEYWORDS KEYWORDS Bisect Bisect P Bisect the line from the point to the centre
KEYWORDS KEYWORDS Bisect Bisect P Construct a circle with the diameter from the centre of the circle to the point P.
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection Point of Point of Contact Contact TANGENT P The intersection (x2) of the new circle with the original circle is the Point of Contact of a tangent drawn from P
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection Point of Point of Contact Contact TANGENT NORMAL Normal Normal P Tangent Tangent A triangle constructed in a semi-circle makes up the normal and tangent
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection Point of Point of Contact Contact TANGENT NORMAL Normal Normal P Tangent Tangent A triangle constructed in a semi-circle makes up the normal and tangent
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection POINT OF CONTACT Point of Point of Contact Contact TANGENT NORMAL Normal Normal P Tangent Tangent
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection POINT OF CONTACT Point of Point of Contact Contact TANGENT NORMAL Normal Normal P Tangent Tangent
KEYWORDS KEYWORDS Bisect Bisect Intersection Intersection Point of Point of Contact Contact Example 1: pg 98 Normal Normal Understanding Technical Graphics Tangent Tangent
Lets make definitions for our keywords Let s make definitions for our keywords Bisect Bisect Intersection Intersection Point of Contact Point of Contact Normal Normal Tangent Tangent
