Math Problem Statement

Let ABC be a triangle, such that AC = 3, BC = 5, AB = 7 and its each side is the diameter of a semicircle. Let S1, S2, S3 be the areas of the grey parts. What is the value of S1 + S2 - S3?

Solution

Let's take a look at the image you uploaded and go over the mathematical problems presented.

We will start with Problem 2.192, which asks for the difference between the areas of the grey parts S1−S2−S3S_1 - S_2 - S_3, where a triangle ABCABC with sides AC=3AC = 3, BC=5BC = 5, and AB=7AB = 7 is inscribed in a semicircle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Shapes
Triangles
Semicircles

Formulas

Area of a triangle = 1/2 * base * height
Area of a circle = πr^2
Pythagoras theorem: a^2 + b^2 = c^2

Theorems

Pythagorean Theorem
Area formulas for triangles and circles

Suitable Grade Level

Grade 10-12

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