UIBezierPath-cutout.swift

import UIKit

let containingRect = CGRect(x: 0, y: 0, width: 100, height: 100)
let path1 = UIBezierPath(rect: containingRect)

let circleRect = CGRect(x: 50, y: 10, width: 80, height: 80)
let circleCenter = CGPoint(x: circleRect.midX, y: circleRect.midY)
let radius = circleRect.height / 2

/*
 +------------------------------------------------------------+
 |                                                            |
 |                                                            |
 |                                                            |
 |                                            .-----------.   |
 |                                       _.--'             `--X.
 |                                     ,'                    /| `.
 |                                   ,'                     / |   `.
 |                                 ,'                      /  |     `.
 |                                /                       /   |       \
 |                               /                 radius/    |b       \
 |                              ;                       /     |         :
 |                              ;                      /      |         :
 |                             ;                      /       |          :
 |                             |                     /alpha   |          |
 |                             |                   -X---------+          |
 |                             :                         a    |          ;
 |                              :                             |         ;
 |                              :                             |         ;
 |                               \                            |        /
 |                                \                           |       /
 |                                 \                          |      /
 |                                  `.                        |    ,'
 |                                    `.                      |  ,'
 |                                      `.                    |,'
 |                                        `---.           _.--'
 |                                             `---------'    |
 |                                                            |
 |                                                            |
 |                                                            |
 +------------------------------------------------------------+
 */
// Compute angle alpha
let a = containingRect.maxX - circleCenter.x
let b = (radius * radius - a * a).squareRoot()
let alpha = Measurement(value: Double(atan(b/a)), unit: UnitAngle.radians)
alpha.converted(to: .degrees)

let path2 = UIBezierPath()
let startAngle = alpha
let endAngle = Measurement(value: 360, unit: .degrees) - alpha
path2.addArc(withCenter: circleCenter,
             radius: radius,
             startAngle: CGFloat(startAngle.converted(to: .radians).value),
             endAngle: CGFloat(endAngle.converted(to: .radians).value),
             clockwise: true)
path2

path1.append(path2.reversing())
path1