How many groups of special angles are related to circles
3
those with measure equal to half the intercepted what
arc
those with measure equal to half the what of the intercepted arcs
sum
those with measure equal to half the what of the intercepted arcs
difference
What has its vertex at the center of the circle
central angle
an angle with sides containing the endpoints of an arc and with a vertex that is a point of the arc other than an endpoint of the arc
Inscribed angle
an angle intercepts an arc if the endpoints of the arc lie on the sides of the angle and all points of the arc except the endpoints lie in the interior of the angle
Intercepted arc
The measure of an inscribed angle is equal to half the measure of its intercepted arc.
Theorem 7-10
An angle inscribed in a semicircle is a right angle.
Corollary 1
The opposite angles of an inscribed quadrilateral are supplementary.
Corollary 2
If two angles intercept the same or equal arcs, the angles are equal.
Corollary 3
a ray that lies on a secant line and contains both points of intersection with the circle
Secant ray
a ray that lies on a tangent line and contains the point of tangency.
Tangent ray
The measure of an angle formed by a secant ray and a tangent ray drawn from a point on a circle is equal to half the measure of its intercepted arc.
Theorem 7-11