Inscribed Angle Theorem (V1)

The PINK ANGLE is said to be an INSCRIBED ANGLE of a circle. You can move the pink point anywhere on the NON-BLUE arc of the circle. You can change the size of the BLUE intercepted arc by moving either of the white points. You can also adjust the circle's radius using the GRAY POINT. Answer the questions that follow.


Without looking up the definition on another tab in your internet browser, how would you describe (define) the concept of an inscribed angle of a circle?


How many inscribed angles fit inside the blue central angle that intercepts (cuts off) the same arc?


Given your result for (2), how does the measure of the pink inscribed angle compare with the measure of the blue intercepted arc?


Try testing your informal conclusions for (responses to) (2) and (3) a few times by dragging the slider back to its starting position, changing the location of the pink inscribed angle, and changing the size of the blue intercepted arc. Then slide the slider again. Do your conclusions for (2) and (3) ALWAYS hold true?

Quick (Silent) Demo