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Intercepted Arc:
• An arc whose endpoints are the two points of intersection of an angle with the circle and all points that lie within the angle.
72˚
If two inscribed angles intercept the same arc, then they are congruent.
Find the measure of DOG and DIG D
O
G
I
If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.
Circumscribed Circle• The circumscribed circle (or
circumcircle) of a polygon is a circle which passes through all the vertices of the polygon.
• The center of this circle is called the circumcenter and its radius is called the circumradius.
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
diameter
4x – 14 = 90
H
K
GN
Example 4
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
x = 26
Bonus: What type of triangle is this? Why?