Unit 8

Tangents on a circle - a line that hits the circumference

Radius - line from centre of circle to any point on the cirumference 

Tangets and Radius of the same circle always meet at 90' ( a right angle)

Two radii (plural of radius) always from an isosceles triangle because any radii in a circle would be the same. They would form equal angles at the circumference points.

In a circle, there will not be lines to mark that there are isosceles triangle present but if two radii join, then an isosceles is definately present.

• A chord is a line drawn across a circle (in the circle).
• If you perpendicually bisect that chord, it will always go through the centre of the circle.
• No matter where the chord is, the perpendicular bisector of the chord will always.

• The angle at the centre of a triangle is twice the angle at the circumference
• The first triangle (angle at circumference) is a random triangle in the circle
• The second triangle (angle at centre) is from the base of the first triangle, joining up at the centre of the circle

When the diameter is drawn in a circle, if two lines are drawn from each end of the diameter, the angle drawn will always be 90'.  The two lines can be drawn to any point on the semi circle, as long as they are from the ends of the diameter

When a chord is drawn in a circle, any triangle on the same side of that chord will be the same where they touch the circumference. However, when two triangles are on each side of the chord, the angle at the circumference will equate to 180'.  

When a quadrilateral is drawn in a circle and each corner of the quadrilateral touches the circumference, opposite interior angles in that quadrilateral will always add up to 180'.

When two tangents from the same point are drawn, they become equivalent in length. This means if you join the point from where the tangents are drawn from to the centre of the circle, two congurent triangles form

The angle between a tangent and chord is equal to the angle in the angle in the opposite segment which is a random triangle with that particular chord as the base. The angle is the angle in line with the angle between the tangent and chord.