10.4: angles formed by secants and tangents

10.4: Angles formed by Secants and Tangents

Obj: ________________________________________________

Vertex is ON the circle

• 1) 2)

Vertex is INSIDE the circle

• 1)

Vertex is OUTSIDE the circle

• 1) 2)

3)

Theorem• If a tangent and a secant (or a chord) intersect

on a circle at the point of tangency, then the measure of the angle formed is __________ the measure of its intercepted arc.

Ex:

Theorem

• The measure of an angle formed by two secants or chords intersecting in the interior of a circle is _______________ the ______________ of the measures of the intercepted arcs.

• The measure of an angle formed by two secants in the exterior of a circle is __________ the measures of the intercepted arcs.

• The measure of a secant-tangent angle with its vertex outside the circle is ____________

_____________________________________

• The measure of a tangent-tangent angle with • its vertex outside the circle is ____________• _____________________________________