Geometry – Lines in circles

In this lesson we will learn:

• Secant and tangent lines: Some lines cross circles twice, others touch them only once
• Congruent tangents: Prove that tangents from the same point are congruent
• Circumscribed angles: Discover how angles between tangents are related to arcs
• Parallel chords: Prove that the arcs between them are always congruent
• Intersecting chords: Discover a rule for how intersecting chords relate
• Cyclic quadrilaterals: See how their opposite angles are related!
• Intersecting secants: Like chords, intersecting secants are also related!
• Inscribed circles: Calculate the radius of any inscribed circle

Chord is any line segment between two points on a circle.
Secant is a line passing through two points on a circle.
Tangent is a line passing though one point on a circle.
Radius are any line segment between a circle and its center.
From any point, the two tangents are always congruent.
Circumscribed angles is an angle between two tangents to a circle.
A circumscribed angle is always supplementary to its arc.
Arc is part of a circle’s circumference between two points.
Diameter is any chord that passes through the center.
An inscribed angle has a vertex on the circumference.
Arcs between parallel chords are always congruent.
Cyclic quadrilaterals are quadrilaterals whose four corners or vertices, are all on the same circle.
In every cyclic quadrilateral, opposite angles are supplementary.
The Inscribed circles or incircle of a triangle is tangent to all three sides.

Geometry – Lines in circles - Secant and tangent lines | Congruent tangents | Circumscribed angles: 

Geometry – Lines in circles - Parallel chords | Intersecting chords: 

Geometry – Lines in circles - Cyclic quadrilaterals | Intersecting secants: 

Geometry – Lines in circles - Inscribed circles: