Prove2Me

The intersection of a unit circle and a tangent line

Proved
WorkbookSource.problem_9565

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

The system of equations: {x2+y2=1 3x+4y=5\begin{cases}x^2+y^2=1 \ 3x+4y=5\end{cases}

Source: InternLM Lean-Workbook, record lean_workbook_9565 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_9565 (x y : ℝ) (h₁ : x ^ 2 + y ^ 2 = 1) (h₂ : 3 * x + 4 * y = 5) : x = 3 / 5 ∧ y = 4 / 5  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9565; Apache-2.0

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