Geometry

Properties of Circles

Circles - Inscribed Angles

         

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

The above diagram shows a circle of radius r,r, with ABC=15.\angle ABC=15^\circ. If the length of arc AC^\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 OO is the center of the circle. If BDC=26,\angle BDC=26^\circ, what is BCA\angle BCA in degrees?

Note: The above figure is not drawn to scale.

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

Note: The above figure is not drawn to scale.

In the diagram above, lines ABAB and BCBC are tangent lines of a circle, with points AA and CC as their respective tangent points. If ADC=70,\angle ADC=70^\circ, what is ABC\angle ABC in degrees?

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