Because of the symmetrical nature of a circle, there are several relationships between angles,lines and circles.
Angle between a Radius and a Tangent
The angle where a radius and a tangent meet is always a right angle.
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∠ABC = 90º
Can b abbreviated to: (rad. perp. tang.) |
Angle in a Semi-circle
The angle in a semi-circle is always 90º, a right angle.
Abbreviated to: ( ∠in a semi-circle).
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In each circle AC is a diameter ∠ABC = 90°
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Triangle formed by Two Radii
Any two radii and a chord will form an isosceles triangle.
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e.g.
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AC and BC are both radii. Triangle ABC is an isosceles triangle. ∠a = ∠b Abbreviated to: (base ∠s of isos. Δ ) |
Tangents from a Point to a Circle
Any two tangents from a point to a circle are equal in length.
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e.g.
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Length of AB = Length of AC AD is an axis of symmetry. ∠a = ∠b |
