olymmath

HMMT 2025 U31

  • Guts
  • Answer

There exists a unique circle that is both tangent to the parabola y=x2y = x^{2} at two points and tangent to the curve x=y31−yx = \sqrt{\frac{y^{3}}{1 - y}} . Compute the radius of this circle.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{\sqrt{5}}{2}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Similar problems

These problems have the most words in common with this statement.

Locator hmmt/2025/u31 · Tag 8ZQT25N1GJ · Edit this page on GitHub · Keys: j next, k previous