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Q1. If two circles have radii of 3 cm and 4 cm, what is the distance between their centers if they are externally tangent?
Solution:
The distance between the centers of two externally tangent circles is the sum of their radii: 3 cm + 4 cm = 7 cm.
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Q2. If two triangles are congruent, which of the following is true?
Solution:
Congruent triangles have the same shape, area, and perimeter.
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Q3. What is the length of the hypotenuse of a right triangle with legs of length 3 cm and 4 cm?
Solution:
Using the Pythagorean theorem, c² = a² + b², we have c² = 3² + 4² = 9 + 16 = 25, so c = 5 cm.
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Q4. What is the radius of a circle if the area is 50π square units?
Solution:
Area of a circle = πr². Setting 50π = πr² gives r² = 50, so r = √50 = 5√2, approximately 7.07 units.
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