LondonEyeBig.JPGBecause 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.

e.g. Y9_Angles_in_Circles__01.gif

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).


In each circle

AC is a diameter

ABC = 90°




Triangle formed by Two Radii

Any two radii and a chord will form an isosceles triangle.

e.g. Y9_Angles_in_Circles__05.gif

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.



Length of AB = Length of AC

AD is an axis of symmetry.

a = b