Olympiad Maths Prep

Track / Stage 4 / 213 of 340 #473 of 2000

Problem 473

AMC 12 late, AIME early
Geometry Difficulty 4.8 Find the answer

28. In Figure 14, there are three circles with radii of 5 cm, 4 cm, and 3 cm, respectively. The area of the overlapping part AA of the two smaller circles compared to the area of the shaded part, which is larger? AA part area \qquad shaded part area. (Fill in “>”, “<” or “=”.)

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

Reference answer: =

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.