[Exercise- Page 180]
E.7.1. O is the center of the circle. The chord PQ = x cm and OR 丄 PQ.
a) What is the measure of ∠QOS?
b) If OR = x2 - 2 cm, determine the value of x.
Solution:
E.7.2. Parallel chords PQ and RS of length 10 cm and 24 cm are on opposite sides of the center of the circle whose center is at O. If the distance between the chords PQ and RS is 17cm, calculate the radius of the circle.
Solution:
E.7.3. Suppose you have a triangular piece of land. The perimeter of the land is 124 meters. You want to cultivate vegetables in the maximum area of that land. If the perimeter of the vegetable garden is 84 m, find the area of the plot.
Solution:
E.7.4. In the figure, O is the center of the circle and TA and TC are two tangents. If ∠ATC = 60°, determine the values of the angles x, y and z.
Solution:
E.7.5. Collect several one (1) tk. coins of the same size (of the same type). Place any one of the coins in the center of your notebook. Now place the coins touching each other around it as shown in the picture. It’s like arranging pieces on a carrom board.
a) Touching in the way shown in the figure, what is the maximum number of coins that can be placed around the coin marked ‘x’? Solve the diagram by completing it.
b) Join the centers of the three circles marked ‘1’, ‘2’ and ‘x’ in the given figure. Suppose the perimeter of the triangle obtained is 18 cm. Using this information, find the area of the green part of the figure.
c) Using any of the coins draw a circle on your notebook. Then find the center of the circle.
d) Draw two circles whose radii are multiples of the radius of any coin. If two circles are tangent to each other on the outside, prove that the distance between the centers of the two circles is twice their average radius.
Solution:
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