Tangent Lines Prepswift Q2

GRE Quant Problem Solving
1

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In this question, why can’t we infer that side CR > RQ?

  • ∠CPR = 60; ∠RPQ = 30. Shouldn’t the sides opposite to these angles must also be somewhat proportional/relative?

Is the reason that △CRP !~ △RQP?

2

You can’t compare this directly for 2 different triangles.

Hint: Try imagining a very huge triangle with a lesser angle. The length will be a lot, with a corresponding smaller angle. That property holds true only within the triangle (then angles and the corresponding sides of the same triangle).