Warm upâ¦

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# Warm upâ¦ - PowerPoint PPT Presentation

Warm up…. Page 543 quiz #’s 1 – 6, 9, 10. 10-4 Inscribed Angles. 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.

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Presentation Transcript
Warm up…
• Page 543 quiz

#’s 1 – 6, 9, 10

### 10-4 Inscribed Angles

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

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

### 10-6 Secants, Tangents and Angle Measure

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)

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

Examples: Find x

40°

6x

55°

141°

x

62°

Assignment:
• Page 549 #13-16 all
• Page 564 # 13-27 odd