MHB Is triangle ANC and isosceles triangle and why

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To determine if triangle ABC is isosceles, the lengths of its sides AB, BC, and AC must be calculated using the distance formula. The distances are found to be AB = √((7 - (-1))² + ((-2) - (-8))²), BC = √((-1 - 5)² + ((-8) - 0)²), and AC = √((7 - 5)² + ((-2) - 0)²). After calculating, if any two sides are equal, the triangle is classified as isosceles. The discussion focuses on verifying the equality of these side lengths. The conclusion will confirm whether triangle ABC is isosceles based on the calculated distances.
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is this triangle isosceles
A(7,-2)
B(-1,-8)
C(5,0)
 
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use the distance formula to calculate the lengths of AB, BC, and AC and find out ...
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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