Module 10: Circles
Topic 2 Application: Central and Inscribed Angles Problem Set
3.

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The final answer is $49$ .

Steps

Step 1 ：Observe the triangle with side lengths 2, 3, and 4. The angle opposite the side of length 2 is $\frac{α}{2}$ .

Step 2 ：Apply the Law of Cosines to this triangle: $2^{2} = 3^{2} + 4^{2} - 2 \cdot 3 \cdot 4 \cos \frac{α}{2}$ .

Step 3 ：Rearrange the equation to solve for $\cos \frac{α}{2}$ : $21 = 24 \cos \frac{α}{2}$ which simplifies to $\cos \frac{α}{2} = \frac{7}{8}$ .

Step 4 ：Use the double angle formula $\cos 2 θ = 2 \cos^{2} θ - 1$ to find $\cos α$ . Substituting $\frac{7}{8}$ for $\cos \frac{α}{2}$ gives $\cos α = \frac{17}{32}$ .

Step 5 ：The sum of the numerator and denominator of $\cos α$ is 17 + 32 = 49.

Step 6 ：The final answer is $49$ .

Module 10: CirclesTopic 2 Application: Central and Inscribed Angles Problem Set3.

Answer

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Module 10: Circles
Topic 2 Application: Central and Inscribed Angles Problem Set
3.