INSCRIBED ANGLES AND

INTERCEPTED ARCS

by: Hilda D. Dragon

Baquilan Resettlement High School

LEAST MASTERED SKILLS:Inscribed Angles and

Intercepted Arcs

SUB TASKS:

1. Identify inscribed angles and their intercepted arcs

2. Apply the key concept of inscribed angles and intercepted arc

3. Solve real-life problems involving inscribed angles and intercepted arcs

GUIDE CARD

OVERVIEWWhat is an Inscribed Angle?

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

What is an Intercepted Arc?It is an arc that lies in

the interior of an inscribed angle and has endpoints on the angle.

I

If an angle is inscribed in a circle, then the

measure of the angle equals one-half the

measure of its intercepted arc.

C

To check, m∟ABC=½ mAC =½ (86 )

=43

A

B 86 43

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If two inscribed angles of a circle intercept congruent arcs or the same arc, then the angles are congruent.

C

D

In the figure ∟CAD and ∟CBD intercept CD. Therefore, m∟CAD=m∟CBD.

If m∟CAD=45 then m∟CBD=45 .

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If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.

Then m∟ABC=90 . Let’s try apply it to find x . The triangle angle sum theorem explains that…………. m∟A +m∟B +m∟C = 180 Substituting the value, 50 + 90 + x = 180 140 + x = 180

x = 180 -140 x = 40

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

Using the figure, to find the m∟F it will be: m∟D = m∟F 85 = m∟F

ACTIVITY CARDActivity 1. Find Me!

1. Name all the inscribed angles in the figure.

2. Which inscribed angles intercept the following arcs?

a. AB

b. CD

C

D

Very Good! Try the next one

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Activity 2. Let’s Practice!

1. Given Circle with circle indicated. Find x.

Choose:

____ 36  ____ 54 ____ 90

____ 108

2. Given the diameter. Find x.

Choose:

 _____ 45 _____ 60 _____ 90

_____ 180

3. Given the diameter. Find x.

Choose:

____   28 ____  56 ____ 62 ____ 124

Activity 3. Measure Me!

1. If m∟A = 45 , find: a. m∟B, why?

b. mCD, why?

2. If m AB = 30 , find: a. m∟1, why?

b. m∟2, why?

:

1

2

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C

D

Wow, good job……try the next

YYou can do this

Activity 4. Half, Equal or Twice As?

1. Which inscribed angles are congruent? Why?

2. If m∟CBD=54, what is the measure of CD?

3. If m∟ABD=5x+3 and m∟DCA=4x+10, finda. the value of x c. m∟DCAb. m∟ABD d. mAD

4. If m∟BDC=6x-4 and mBC=10x+2, find:a. the value of x c.mBCb. m∟BDC d. m∟BAC

E

D

C

B

A

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Very good! Now you’re ready

ASSESSMENT CARD

I believe I can do this…

Direction: Use the given figures to answer the following.

1. CAR is inscribed in circle E. If m∟C=80 and mRC= 150, find:

a. mAR b. mAC c. m∟A d. m∟R

2. HD is a diameter of circle O. If mRD = 70 , find: a. m∟H c. m∟Rb. m∟D d. mRHe. mHD

.E

C

A

R

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.O

R D

H

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3. Quadrilateral HOPE is inscribed in circle S. If m∟HOP = 80 and m∟OPE=75, find:

a. m∟PEHb. m∟EHO

4. Isosceles YOUis inscribed in circle R.IfmUO=120 ,

find: a. m∟YOUb. m∟YOUc. mYU d. mYO

H.SE

P

O

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Y

O

U

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Well done…Good job!!!

ENRICHMENT CARD

Activity : Take Me To Your Real World !Answer the following questions.

1. What kind of parallelogram can be inscribed in a circle? Explain.

2. There are circular garden having paths in the shape of an inscribed square like one shown below.a. Determine the measure of an arc intercepted by an inscribed angle formed by the square in the garden.

b. What is the measure of an inscribed angle in a garden in a garden with a square? Explain.

REFERENCE CARD

Learner’s Module , First Edition 2015 pp. 165-175Callanta, Melvin. et al.

Geometry, Third Year pp. 205-207Bernabe, Julieta. et al

http://www.iq.poquoson.org/math.htm

http://www.math-worksheets.org/inscribed -angles

http://www.onlinemathlearning.com/circle-theorems.html