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Geometry

# Solving Triangles: Level 2 Challenges

If the angles of a triangle are in ratio 4:1:1, then the ratio of longest side to perimeter is:

In the figure, $$\triangle ABC$$ is an equilateral triangle where $$AB = 6$$ cm. The area of the circumcircle is $$k\pi$$ cm$$^{2}$$. Find the value of $$k$$.

If $$CD=\sqrt{3},$$ $$PQ=2,$$ and $$\angle PDQ=30^\circ,$$ find $$CP.$$

In triangle $$ABC$$, $$\angle BAC = 2 \angle ABC$$, $$AB= 31, AC = 13$$. What is $$BC^2$$?

If $$AP = AC + 2\cdot CB$$, what is the measure $$\angle ABP$$ in degrees?

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