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Circle Theorems Part 3 - Tangents

Circle Theorems Part 3 - Tangents. O. Definition A tangent is a line which just touches the circumference of the circle once. O. Tangent Theorem 1 The radius drawn to the point of contact makes a right angle. Tangent Theorem 2

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Circle Theorems Part 3 - Tangents

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  1. Circle Theorems Part 3 - Tangents

  2. O Definition A tangent is a line which just touches the circumference of the circle once.

  3. O Tangent Theorem 1 The radius drawn to the point of contact makes a right angle.

  4. Tangent Theorem 2 From any external point only two tangents can be drawn and they are of equal length. O

  5. These two angles are also equal These two angles are equal Alternate Segment Theorem The angle between a tangent and a chord at the point of contact is equal to the angle subtended by the chord in the alternate segment.

  6. x O 90-x Proof C D Draw a diameter AD. x Angle DAT = 90 Angle DAB = 90 - x B Angle DBA = 90 Angle ADB = x Angle ACB = x x A T

  7. O Example C a a = 70 (AST) b = 180 – 50 – 70 = 60 B b c = b = 60 (AST) 50 c 70 A T

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