diff --git a/src/circle.ts b/src/circle.ts
index 78412eb..d60eda8 100755
--- a/src/circle.ts
+++ b/src/circle.ts
@@ -47,6 +47,12 @@ export class Circle implements GeoShape {
     return d <= this.r;
   }
 
+  /** Whether the given line intersects this circle */
+  intersect(l: Line) {
+    const closest = l.project(this.c);
+    return Point.distance(closest, this.c) < this.r;
+  }
+
   // ---------------------------------------------------------------------------
 
   project(p: Point) {
diff --git a/src/overlap.ts b/src/overlap.ts
new file mode 100644
index 0000000..6e10f10
--- /dev/null
+++ b/src/overlap.ts
@@ -0,0 +1,166 @@
+// =============================================================================
+// Euclid.js | Overlap utilities
+// (c) Mathigon
+// =============================================================================
+
+import {Circle} from './circle';
+import {intersections} from './intersection';
+import {Line, Segment} from './line';
+import {Point} from './point';
+import {Polygon} from './polygon';
+import {GeoElement, GeoShape} from './utilities';
+
+
+/** Whether two GeoElements overlap */
+export function overlap(a: GeoShape | Point | GeoElement, b: GeoShape | Point | GeoElement) {
+  if (isGeoShape(a)) {
+    if (isGeoShape(b)) {
+      return geoShapeOverlap(a, b);
+    } else {
+      return contains(a, b);
+    }
+  }
+  if (a instanceof Point) {
+    if (b instanceof Point) {
+      return Point.equals(a, b);
+    }
+    if (isGeoShape(b)) {
+      return contains(b, a);
+    }
+  }
+  return false;
+}
+
+export function contains(a: GeoShape, b: GeoElement) {
+  if (b instanceof Point) {
+    return a.contains(b);
+  } else {
+    return false;
+  }
+}
+
+function geoShapeOverlap(a: GeoShape, b: GeoShape) {
+  if (a instanceof Polygon) {
+    if (b instanceof Polygon) {
+      for (const bEdge of b.edges) {
+        for (const aEdge of a.edges) {
+          if (lineLineOverlap(bEdge, aEdge)) return true;
+        }
+      }
+    }
+    if (b instanceof Line) {
+      for (const edge of a.edges) {
+        if (lineLineOverlap(edge, b)) return true;
+      }
+    }
+    if (b instanceof Circle) {
+      return polygonCircleOverlap(a, b);
+    }
+  }
+  if (a instanceof Line) {
+    if (b instanceof Polygon) {
+      for (const edge of b.edges) {
+        if (lineLineOverlap(edge, a)) return true;
+      }
+    }
+    if (b instanceof Line) {
+      return lineLineOverlap(a, b);
+    }
+    if (b instanceof Circle) {
+      return b.intersect(a);
+    }
+  }
+  if (a instanceof Circle) {
+    if (b instanceof Polygon) {
+      return polygonCircleOverlap(b, a);
+    }
+    if (b instanceof Line) {
+      return a.intersect(b);
+    }
+    if (b instanceof Circle) {
+      return circleCircleOverlap(a, b);
+    }
+  }
+  // TODO: Handle others
+  return false;
+}
+
+function circleCircleOverlap(a: Circle, b: Circle) {
+  return Point.distance(a.c, b.c) < a.r + b.r;
+}
+
+function polygonCircleOverlap(poly: Polygon, circ: Circle) {
+  for (const edge of poly.edges) {
+    if (circ.intersect(edge)) return true;
+  }
+  return false;
+}
+
+function lineLineOverlap<A extends Line, B extends Line>(a: A, b: B): boolean {
+  if (a instanceof Segment) {
+    if (b instanceof Segment) {
+      return segmentSegmentOverlap(a, b);
+    } else {
+      return segmentLineOverlap(a, b);
+    }
+  } else if (b instanceof Segment) {
+    return segmentLineOverlap(b, a);
+  } else if (a.equals(b)) {
+    return true;
+  } else {
+    return intersections(a, b).length > 0;
+  }
+  // TODO: handle rays
+}
+
+function segmentLineOverlap(a: Segment, b: Line) {
+  const p1 = b.project(a.p1);
+  const p2 = b.project(a.p2);
+  const s = new Segment(p1, p2);
+  return segmentSegmentOverlap(a, s);
+}
+
+function segmentSegmentOverlap(a: Segment, b: Segment) {
+  const o1 = getOrientation(a.p1, a.p2, b.p1);
+  const o2 = getOrientation(a.p1, a.p2, b.p2);
+  const o3 = getOrientation(b.p1, b.p2, a.p1);
+  const o4 = getOrientation(b.p1, b.p2, a.p2);
+
+  if (o1 !== o2 && o3 !== o4) {
+    return true;
+  } else if (o1 === 'collinear' && a.contains(b.p1)) {
+    return true;
+  } else if (o2 === 'collinear' && a.contains(b.p2)) {
+    return true;
+  } else if (o3 === 'collinear' && b.contains(a.p1)) {
+    return true;
+  } else if (o4 === 'collinear' && b.contains(a.p2)) {
+    return true;
+  } else {
+    return false;
+  }
+}
+
+function isGeoShape(o: GeoElement | GeoShape): o is GeoShape {
+  if ('project' in o && typeof o.project === 'function') {
+    return true;
+  }
+  return false;
+}
+
+type Orientation =
+  'clockwise' |
+  'counterclockwise' |
+  'collinear';
+
+// Based on: https://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
+function getOrientation(a: Point, b: Point, c: Point): Orientation {
+  const val = (b.y - a.y) * (c.x - b.x) - (b.x - a.x) * (c.y - b.y);
+  if (val === 0) {
+    return 'collinear';
+  } else if (val > 0) {
+    return 'clockwise';
+  } else {
+    return 'counterclockwise';
+  }
+}