import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_algebra_288
  (x y : ℝ)
  (n : NNReal)
  (h₀ : x < 0 ∧ y < 0)
  (h₁ : abs y = 6)
  (h₂ : Real.sqrt ((x - 8)^2 + (y - 3)^2) = 15)
  (h₃ : Real.sqrt (x^2 + y^2) = Real.sqrt n) :
  n = 52 := by sorry