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 intercepted arc.

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. Due to 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 consecutively like an arc of a circle. Joanna, Clarissa, and Juliana entered the movie house but seated away from each other as shown below.

Let E and G be the ends of the screen and 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 center of 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’s square, draw a line that is exactly 90 degrees to the chord pointing towards the center of the circle. Make it a little longer. The center of the circle is the point where all of these perpendicular lines intersect. Step-by-step pictures below:

Step 1: Draw some chords.

Step 2: Mark the centers and draw a perpendicular line.

Step 3: The center is 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.

b. How is RS related to PS and QS? Justify your answer. The length of segment RS 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-2 inches=6 inches) and the measure of QS is 2 inches (8 inches-6 inches=2 inches). Remembering the 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.