10.4

Inscribed Angle: an angle that has a vertex on the circle. The sides of the angles are chords.

Intercepted Arc: the arc that is contained in the inscribed arc.

The measure of the arc is half the size of the inscribed angle.

If we want to find the measure of arc QT, what do we do with the measure of the inscribed angle óTRQ?

QTmTRQm2

1

QTm2

150 Multiply both sides by

2

QTm2

12502 Simplif

y

QTm100

100º

92º

=46º

The arc is twice the inscribed angle

172ºA circle is 360º

360 – 84 – 172 = 104º

86º

84º

DGm

104º

A semi-circle is 180º

180 – 125 = 5510º

The inscribed angle is half the arc.

115ºO55º27.5º

MNOm

RSm )(2 SURm 62)31(2 )(2 STRmRSm

)(262 STRm31STRm

With this theorem we basically know that there are 2 proportional triangles.

Recall that proportional triangles have congruent angles.

18024 bb

1806 b30b

Don’t forget that opposite angles in

an inscribed quadrilateral are supplementary!

Supplementary is 180

18022 aa

1804 a45a

95+ q = 180

q = 85

P + 110= 180

p= 70