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Mathematics 22 Online
OpenStudy (anonymous):

What is the relationship among inscribed angles, radii, and chords?

OpenStudy (anonymous):

@ShelbyWyatt

OpenStudy (shelbywyatt):

hmm

OpenStudy (anonymous):

doesnt tell me about the radii @ShelbyWyatt

OpenStudy (shelbywyatt):

:(

OpenStudy (adrimit):

there are many parts to your question. First, an inscribed angle subtending an arc has as its value exactly half that of the central angle

OpenStudy (adrimit):

the central angle has the center of the circle as its vertex

OpenStudy (shelbywyatt):

a radii is a line start from the middle of the circles to any point on the circumference of the circcle

OpenStudy (shelbywyatt):

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle.

OpenStudy (adrimit):

two intersecting chords form two pairs of vertical angles. select one of these pairs. the arcs subtended by this pair have as their sum in radians twice the chosen angle. to see this, let the chords be diameters.

OpenStudy (adrimit):

if a pair of non intersecting chords is chosen, the angle subtending both chords (vertex outside the circle) is half the difference of the subtended arcs in radians

OpenStudy (shelbywyatt):

why so hard...

OpenStudy (adrimit):

also note that a right triangle can always be inscribed in a circle with its hypotenuse as a diameter

OpenStudy (adrimit):

this illustrates that the central angle defined by the hypotenuse \[i.e. \pi\] is twice the inscribed angle \[i.e. \frac{\pi}{2}\]

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