## Euclid 2024 Question 7, CEMC UWaterloo

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#### Difficulty: 8

#### This problem is tagged with euclid, euclid24, highschool.

**(Euclid 2024, Question 7, CEMC - UWaterloo)**

(a) Arun and Bella run around a circular track, starting from diametrically opposite points. Arun runs clockwise and Bella runs counterclockwise. Arun and Bella run at constant, but different, speeds. They meet for the first time after Arun has run $100$ m. They meet for the second time after Bella runs $150$ m past their first meeting point. What is the length of the track?

(b) Determine all angles $\theta$ with $0^{\circ} \leq \theta \leq 360^{\circ}$ for which $4^{1+\cos^3 \theta}=2^{2-\cos \theta} \cdot 8^{\cos^2 \theta}$.

*Answer Submission Note(s)*

In part (b), sort your answers in ascending order and separate them with a comma.

Separate the answers for each part with a single space.

Do not include any units.

For example: "a b1,b2"

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