A sample answer on Mathematics 10: Activity 11: Take Me to Your Real World!, 2nd Quarter

1. Sophia Marie D. Verdeflor Grade 10-1 STE
TAKE ME TO YOUR REAL WORLD!Activity 11:
Answer the following questions.
1. There are circular gardens having paths in the shape of an inscribed regular star like the
one shown above.
a. Determine the measure of an arc intercepted by an inscribed angle formed by the star
in the garden.
 72° (360°÷5=72°); 360°-measure of the circle;5-number of points of the inscribed
regular star
b. What is the measure of an inscribed angle in a garden with a five-pointed star? Explain.
 36° (72°÷2=36°);72°-measure of the intercepted arc; Note:The measure of an inscribed
angle is one-half the measure of its corresponding interceptedarc.
2. What kind of parallelogram can be inscribed in a circle? Explain.
 The kind of parallelogram that can be inscribed in a circle is a rectangle because we
can only draw one chord parallel and congruent to another chord in the same circle.
Dueto observations, the diagonals of the parallelogram can also be the diameter of
the circle.Each inscribed angle formed by the adjacent sides of the parallelogram
intercepts a semicircle with a measure of 90°.
3. The chairs of the movie house are arranged consecutivelylike an arc of a circle.
Joanna, Clarissa, and Juliana entered the movie house but seated away from each other
as shown below.

2. Let E and G be the ends of the screenand F be one of the seats. The
angle formed by E, F, and G or L EFG is called the viewing angle of the
person seated at F. Suppose the viewing angle of Clarissa in the above
figure measures 38°. What are the measures of the viewing angles of
Joanna and Juliana? Explain your answer.
 38° The viewing angles of Joanna, Clarissa and Juliana intercepts the same
arc namely arc EG, so, basically, the measures of the viewing angles of
Joanna and Juliana are also the same with the measure of the viewing angle
of Clarissa because they all intercepts the same arc.
4. A carpenter’s square is an L-shaped tool used to draw right angles.
Mang Ador would like to make a copy of a circular plate using the
available wood that he has. Suppose he traces the plate on a piece of
wood. How could he use a carpenter’s square to find the centerof the
circle?
 Mang Ador needs to draw some chords using the L-shaped tool. Use a ruler
to find the midpoints of the chords that Mang Ador just drew. After locating
the midpoints, draw a perpendicular line. Then,using a carpenter’ssquare,
draw a line that is exactly90 degreesto the chord pointing towards the
centerof the circle. Make it a little longer. The centerof the circle is the
point where all of these perpendicular lines intersect. Step-by-steppictures
below:
Step 1: Draw some chords.
Step 2: Mark the centers and draw a perpendicular line.

3. Step 3: The centeris the point where they intersect
5. Ramon made a circular cutting board by sticking eight 1- by 2-by 10-inch boards
together, as shown on the right. Then,he drew and cut a circle with an 8-inch diameter
from the boards.
a. In the figure, if PQ is a diameter of the circular cutting board, what kind of triangle is L
PQR?
 L PQR is a right triangle because it forms a 90 degrees angle.

4. b. How is RS related to PS and QS? Justify your answer.
 The length of segmentRS is the geometric mean of the length of segment PS and
the length of segment QS.
c. Find PS, QS,and RS.
 PS= 6 inches; QS= 2 inches;RS= 2√3
Since,the measure of the diameter is given which is 8 inches,the measure of PS is 6
inches (8 inches-2inches=6inches) and the measure of QS is 2 inches(8 inches-6
inches=2inches).Rememberingthe 30°-60°-90° Theorem,the long leg is equal to the
short leg multiply the √3.
d. What is the length of the seam of the cutting board that is labeled RT? How about
MN?
 The measure of RT is 4√3 and the measure of MN is 4√3 also.