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HBO and The Ringer's Bill Simmons hosts the most downloaded sports podcast of all time, with a rotating crew of celebrities, athletes, and media staples, as well as mainstays like Cousin Sal, Joe House, and a slew of other friends and family members who always happen to be suspiciously available.
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Welcome to Episode 9 of Season 2: Unlocking Combinatorics and Geometry! This episode discusses various methods for calculating area ratios in triangles, particularly those that appear on the AMC 10 and AMC 12 exams. Several theorems are presented, explaining how area ratios relate to side length ratios based on shared heights, shared bases, or shared angles. The audio includes solved problems demonstrating the application of these theorems to complex geometric figures and area calculations. The problems illustrate strategies for finding the area of a portion of a triangle by subtracting the areas of other triangles or by utilizing the ratio of side lengths surrounding a common angle.
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