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# Squares and Triangles | AIME I, 1999 | Question 4

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and triangles.

## Squares and triangles - AIME I, 1999

The two squares share the same centre O and have sides of length 1, The length of AB is $\frac{43}{99}$ and the area of octagon ABCDEFGH is $\frac{m}{n}$ where m and n are relatively prime positive integers, find m+n.

• is 107
• is 185
• is 840
• cannot be determined from the given information

### Key Concepts

Squares

Triangles

Algebra

AIME I, 1999, Question 4

Geometry Vol I to IV by Hall and Stevens

## Try with Hints

First hint

Triangle AOB, triangleBOC, triangleCOD, triangleDOE, triangleEOF, triangleFOG, triangleGOH, triangleHOA are congruent triangles

Second Hint

with each area =$\frac{\frac{43}{99} \times \frac{1}{2}}{2}$

Final Step

then the area of all 8 of them is (8)$\frac{\frac{43}{99} \times \frac{1}{2}}{2}$=$\frac{86}{99}$ then 86+99=185.

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