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Warm up…

- Page 543 quiz
#’s 1 – 6, 9, 10

Inscribed Angles

- If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of the intercepted arc
- The measure of the intercepted arc is 2 times the measure of the inscribed angle

B

A

D

C

Intercepting the same arc

- If 2 inscribed angles intercept congruent arcs or the same arc then the angles are congruent

A

B

B

A

C

F

D

C

D

E

Angles of inscribed polygons

- If an inscribed angle intercepts a semicircle, the angle is a right angle

A

D

B

C

ADC is a semicircle, so m<ABC = 90°

Example 1:

- mWX=20, mXY=40, mUZ=108 and mUW=mYZ. Find the measures of the numbered angles.

W

X

3

Y

4

5

F

2

U

Z

1

T

Example 2:

- Triangles TVU and TSU are inscribed in circle P, m<2 = x+9 and m<4 =2x+6,
- Find the measure of the numbered angles

U

V

3

4

S

P

1

2

T

Inscribed Quadrilaterals

- If a quadrilateral is inscribed in a circle then its opposite angles are supplementary

Secants

- A line that intersects a circle in exactly 2 points
- When 2 secant lines intersect in the interior of a circle the measure of an angle formed is ½ the sum of the measures of the intercepted arcs and its vertical angle

A

D

m<1 = ½(mAC + mBD)

m<2 = ½(mAD + mBC)

2

1

B

C

Secant and Tangent

- If a secant and a tangent intersect at a point of tangency, then the measure of each angle formed is ½ the measure of the intercepted arc
- Example: Find m<RPS if mPT =114 and mTS = 136

R

P

Q

S

114°

T

136°

Intersection outside a circle

D

- Two secants – m<A = ½(mDE – mBC)
- Secant-tangent – m<A=1/2(mDC – mBC)
- Two tangents – m<A=1/2(mBDC – mBC)

B

A

C

E

D

B

A

C

B

D

A

C

Assignment:

- Page 549 #13-16 all
- Page 564 # 13-27 odd

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