Triangles - Properties and Congruence for Competitive Exams

Triangles - Properties and Congruence - Problems on Circles - Case Studies

Q. If two circles intersect at two points, what can be said about their radii?

Solution

Two circles can intersect at two points regardless of whether their radii are equal or different.

Correct Answer: C — They can be equal or different

Q. In a triangle, if one angle measures 70 degrees and the other measures 50 degrees, what is the measure of the third angle?

Solution

The sum of the angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 70 - 50 = 60 degrees.

Correct Answer: C — 80 degrees

Q. What is the length of the hypotenuse of a right triangle with legs of length 3 and 4?

Solution

Using the Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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