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Form 4 Mathematics
Tangents to a circle
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Definition AB is called a tangent to the circle if it touches the circle at one point only. The touching point P is called the point of contact. |
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Investigation CD is perpendicular to the radius OP. Drag E along OP. When E reaches the point P, is OP perpendicular to CD? What do we called CD in this case? Drag P along the circle, what can you say about CD and OP? Press "r" to reset. |
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Tangents from an external point P is a point outside the circle. Can you use only basic geometric constructions to construct two tangents passing through P? Prove, using known geometric theorems, that your constructions form two tangents. |
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Definition Given PQ is a tangent to the circle at A. The angles CAQ, CAP, BAQ, BAP are all tangent-chord angles. Corresponding to the angle CAQ, the segment ADBC is called the alternate segment ; and the angle ABC is called the angle in the alternate segment. |
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Angle in alternate segment What is the reason for angle BAD = angle BCD ? Drag A towards B. What happens to the line AB when A just reaches B? What is the measure of the angle BAD? |
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