Arcs & AnglesChapter 10

Draw & LabelCentral AngleMinor ArcMajor Arc

k

Central Angles

f Every central angle has a corresponding arc.

Thus, the measure of an arc is equal to its corresponding central angle.

Inscribed AnglesInscribed angle –

an angle whose vertex is on a circle and whose sides contain chords of the circle.

Intercepted arc – the arc that lies in the interior of an inscribed angle and has endpoints on the angle.

f

Measure of an Inscribed AngleIf an angle is inscribed in a circle,

then its measure is half the measure of its intercepted arc.

IN OTHER WORDS….To find the angle of the ARC

(when you are given the measure of the inscribed angle) …. MULTIPLY BY 2!!

To find the measure of the INSCRIBED angle (when you are given the arc angle) …. DIVIDE BY 2!!

Example 1:Find X.

Example 2:Find the measure of arc PQ.

Right Triangles InscribedIf a right triangle is inscribed in a

circle, then the hypotenuse is a diameter of the circle.

Two Inscribed AnglesIf two inscribed angles of a circle

intercept the same arc, then the angles are congruent.

Turn to page pg. 588Work problem 10-16 Do a – fTURN in for a GRADE!Start on worksheet and finish for

homework. I will be checking this tomorrow. OMIT # 18

You will have 2 homework grades tomorrow!