class Point { constructor(x, y) { this.x = x; this.y = y; } } class Circle { constructor(x, y, r) { this.x = x; this.y = y; this.r = r; } } /* * Returns the smallest circle that encloses all the given points. Runs in expected O(n) time, randomized. * Note: If 0 points are given, null is returned. If 1 point is given, a circle of radius 0 is returned. */ // Initially: No boundary points known function makeCircle(points) { // Clone list to preserve the caller's data, do Durstenfeld shuffle let shuffled = points.slice(); for (let i = points.length - 1; i >= 0; i--) { let j = Math.floor(Math.random() * (i + 1)); j = Math.max(Math.min(j, i), 0); const temp = shuffled[i]; shuffled[i] = shuffled[j]; shuffled[j] = temp; } // Progressively add points to circle or recompute circle let c = null; shuffled.forEach((p, i) => { if (c === null || !isInCircle(c, p)) c = makeCircleOnePoint(shuffled.slice(0, i + 1), p); }); return c; } // One boundary point known function makeCircleOnePoint(points, p) { let c = new Circle(p.x, p.y, 0); points.forEach((q, i) => { if (!isInCircle(c, q)) { if (c.r == 0) c = makeDiameter(p, q); else c = makeCircleTwoPoints(points.slice(0, i + 1), p, q); } }); return c; } // Two boundary points known function makeCircleTwoPoints(points, p, q) { const circ = makeDiameter(p, q); let left = null; let right = null; // For each point not in the two-point circle for (const r of points) { if (isInCircle(circ, r)) continue; // Form a circumcircle and classify it on left or right side const cross = crossProduct(p.x, p.y, q.x, q.y, r.x, r.y); const c = makeCircumcircle(p, q, r); if (c === null) continue; else if (cross > 0 && (left === null || crossProduct(p.x, p.y, q.x, q.y, c.x, c.y) > crossProduct(p.x, p.y, q.x, q.y, left.x, left.y))) left = c; else if (cross < 0 && (right === null || crossProduct(p.x, p.y, q.x, q.y, c.x, c.y) < crossProduct(p.x, p.y, q.x, q.y, right.x, right.y))) right = c; } // Select which circle to return if (left === null && right === null) return circ; else if (left === null && right !== null) return right; else if (left !== null && right === null) return left; else if (left !== null && right !== null) return left.r <= right.r ? left : right; else throw new Error("Assertion error"); } function makeDiameter(a, b) { const cx = (a.x + b.x) / 2; const cy = (a.y + b.y) / 2; const r0 = distance(cx, cy, a.x, a.y); const r1 = distance(cx, cy, b.x, b.y); return new Circle(cx, cy, Math.max(r0, r1)); } function makeCircumcircle(a, b, c) { // Mathematical algorithm from Wikipedia: Circumscribed circle const ox = (Math.min(a.x, b.x, c.x) + Math.max(a.x, b.x, c.x)) / 2; const oy = (Math.min(a.y, b.y, c.y) + Math.max(a.y, b.y, c.y)) / 2; const ax = a.x - ox; const ay = a.y - oy; const bx = b.x - ox; const by = b.y - oy; const cx = c.x - ox; const cy = c.y - oy; const d = (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)) * 2; if (d == 0) return null; const x = ox + ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) * (cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d; const y = oy + ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) * (ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d; const ra = distance(x, y, a.x, a.y); const rb = distance(x, y, b.x, b.y); const rc = distance(x, y, c.x, c.y); return new Circle(x, y, Math.max(ra, rb, rc)); } /* Simple mathematical functions */ const MULTIPLICATIVE_EPSILON = 1 + 1e-14; function isInCircle(c, p) { return c !== null && distance(p.x, p.y, c.x, c.y) <= c.r * MULTIPLICATIVE_EPSILON; } // Returns twice the signed area of the triangle defined by (x0, y0), (x1, y1), (x2, y2). function crossProduct(x0, y0, x1, y1, x2, y2) { return (x1 - x0) * (y2 - y0) - (y1 - y0) * (x2 - x0); } function distance(x0, y0, x1, y1) { return Math.hypot(x0 - x1, y0 - y1); } function Main(input) { const lines = input.split('\n').map(x => x.trim()).filter(Boolean); const q = +lines[0]; const [xa, ya, xb, yb, xc, yc] = lines[1].split(' ').map(Number); const circle = makeCircle([ new Point(xa, ya), new Point(xb, yb), new Point(xc, yc), ]); for (let i = 0; i < q; i++) { const [x, y] = lines[2 + i].split(' ').map(Number); const d = Math.hypot(x - circle.x, y - circle.y); const result = d <= circle.r ? 'Yes' : 'No'; console.log(result); } } Main(require("fs").readFileSync("/dev/stdin", "utf8"));