Nov27 Dec216Ma10
Nov27 Dec216Ma10
Nov27 Dec216Ma10
1. Which lines intersect circle C at two points? How about the lines that intersect the circle at exactly one
point?
2. What are the angles having A as the vertex? C as the vertex? D as the vertex? G as the vertex? Make a list
of these angles, then describe each.
3. What arc/s does each angle intercept?4. Which angles intercept the
same arc?
5. Using a protractor, find the measures of the angles identified in item #2?
6. How would you determine the measures of the arcs intercepted by the
angles? Give the degree measure of each arc.
7. Compare the measures of angle DCE and angle DAE. How about the
measure of arc DE and measure of angle DAE? Explain your answer.
8. How is the measure of arc AD related to the measures of
angleDAB? How about measures of arc EFA and measure of angle EAG?
9. What relationship exists among measures of arc AD, measure of AF, and measure of angle BGD?
Were you able to measure the different angles and arcs shown in the figure? Were you able to find out the
different relationships among these angles and arcs? Learn more about these relationships in the succeeding
activities.
IV. Deepen
Discussion of Tangents Angles pp.29 – 46 Do the Time to Think activity pp.28 – 45
LESSON 5 – Relations of Circle and Polygons
I. Preliminaries:
At the end of the lesson, the learner should be able to:
II. Explore
Given two circles. They may intersect or they may not intersect or they may not intersect. Below are the
cases when they do not intersect.
R
Q
P
The circles above are disjoints i.e., one is apart from the other.
The line that joins the centers of two circles is called line of centers.
The tangent common to both circles which does not intersect the line of centers is called common external
tangent. HS is a common external tangent.
The tangent common both circles which intersects the line of centers is called common internal tangent.
´
HK is a common internal tangent.
III. Firm Up
Circles having the same center are called concentric circles.
M A
P x
B
T
It is clearly shown that the arcs they intercept have the following measures.
o o
m∠ APB=x , m∠CPD=x
It follows that the arcs they intercept have the following measures.
m^ ^ =x o
o
AB= x , m CD
These facts clearly demonstrate that the measure of the arc does not depend on the size of the circle.
This means that for arcs to have the same measure they need not have the same length. CD ^ is evidently
longer than ^ AB.
It will likewise be noted that a chord of the bigger circle may be tangent to the smaller circles, as MN .
If two circles intersect, they have at most two points of intersection. The possible cases are illustrated
below.
IV. Deepen
Discussion of Tangents Angles pp.47 – 48
Do the Time to Think activity pp.49 – 50