Geometry

Properties of Circles

Circles - Inscribed Angles

A , B , C A, B, C and D D are consecutive points on a circle (labeled clockwise) such that A B C = 7 3 \angle ABC = 73 ^\circ . What is the measure of A D C \angle ADC (in degrees)?

The above diagram shows a circle of radius r , r, with A B C = 1 5 . \angle ABC=15^\circ. If the length of arc A C ^ \widehat{AC} is equal to 10 , 10, what is the measure of r ? r?

Note:The above figure is not drawn to scale.

In the above diagram, point O O is the center of the circle. If B D C = 2 6 , \angle BDC=26^\circ, what is B C A \angle BCA in degrees?

Note:The above figure is not drawn to scale.

In the diagram above, the measures of the two arcs B C ^ \widehat{BC} and C D ^ \widehat{CD} are equal. If B A C = 2 0 \angle BAC=20^\circ and A B D = 4 0 , \angle ABD=40^\circ, and the measure of arc B C ^ \widehat{BC} is equal to 6 , 6, what is the measure of arc A P B ^ ? \widehat{APB}?

Note:The above figure is not drawn to scale.

In the diagram above, lines A B AB and B C BC are tangent lines of a circle, with points A A and C C as their respective tangent points. If A D C = 7 0 , ADC = 70 ^ \ \角保监会, what is A B C \angle ABC in degrees?

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