AMC 8 Daily Practice - Circles

Complete problem set with solutions and individual problem pages

Problem 1 Easy

A part of a circular glass mirror is damaged. To obtain a mirror of the same size, a worker uses a right-angle ruler for measurement as shown in the figure, and finds that AB = 12cm and BC = 5cm. What is the diameter of the circular mirror in centimeters?

  • A.

    10

  • B.

    11

  • C.

    12

  • D.

    13

  • E.

    14

Answer:D

It is known that the circumferential angle subtended by a diameter is a right angle.

Therefore, connecting AC forms a right triangle ABC with \angle ABC = 90^\circ, and AC is the diameter of the circular mirror.

By the Pythagorean theorem in \triangle ABC: AC = \sqrt{AB^2 + BC^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13

Thus, the diameter of the circular mirror is 13 centimeters.

Related Problems
Problem 2 AMC 8 Daily Practice - Circles
Problem 3 AMC 8 Daily Practice - Circles
Problem 4 AMC 8 Daily Practice - Circles
Problem 5 AMC 8 Daily Practice - Circles
Think Academy Powered by ChatGPT