Drawing circles using CGContext

Question

Using the code below, I am constructing polygons with various number of sides.

Can somebody advise how I can add code to circumscribe a circle and also inscribe a circle in each polygon returned?

-(void) drawRect:(CGRect)rect{
    CGContextRef context = UIGraphicsGetCurrentContext(); 
    CGContextBeginPath (context); 
    CGContextSetLineWidth(context,5);

    NSArray * points = [PolygonUIView pointsForPolygonInRect:[self bounds] numberOfSides:polygon.numberOfSides];

    NSLog(@"%d", [points count]);
    NSLog(@"%d", polygon.numberOfSides);

    for(NSValue * point in points) {
        CGPoint val = [point CGPointValue];
        if([points indexOfObject:point]==0)
        {
            CGContextMoveToPoint (context, val.x, val.y);

        }
        else
        {
            CGContextAddLineToPoint (context, val.x, val.y); 
        }
    }

    CGContextClosePath(context);
    [[UIColor clearColor] setFill]; 
    [[UIColor blackColor] setStroke]; 
    CGContextDrawPath (context, kCGPathFillStroke);
    polygonLabel.text = polygon.name;
}

+ (NSArray *)pointsForPolygonInRect:(CGRect)rect numberOfSides:(int)numberOfSides { 
    CGPoint center = CGPointMake(rect.size.width / 2.0, rect.size.height / 2.0); 
    float radius = 0.90 * center.x; 
    NSLog(@"%f rad",radius);
    NSMutableArray *result = [NSMutableArray array]; 
    float angle = (2.0 * M_PI) / numberOfSides; 
    float exteriorAngle = M_PI - angle; 
    float rotationDelta = angle - (0.5 * exteriorAngle); 

    for (int currentAngle = 0; currentAngle < numberOfSides; currentAngle++) { 
        float newAngle = (angle * currentAngle) - rotationDelta; 
        float curX = cos(newAngle) * radius; 
        float curY = sin(newAngle) * radius; 
        [result addObject:[NSValue valueWithCGPoint:CGPointMake(center.x + curX, 
                                                                center.y + curY)]]; 
    } 

    return result;
}

Answer 1

finally sussed it out thanks to some pointers from others code below added to the original code gives me the result i need thanks

// circumscribe the polygons
CGContextSetLineWidth(context, 2); // set the line width
CGContextSetRGBStrokeColor(context, 20.0 /255, 101.0 / 255.0, 18.0 / 255.0, 1.0);

CGPoint center = CGPointMake(rect.size.width / 2, rect.size.height / 2); // get the circle centre
CGFloat radius = 0.9 * center.x; // little scaling needed
CGFloat startAngle = -((float)M_PI / 2); // 90 degrees
CGFloat endAngle = ((2 * (float)M_PI) + startAngle);
CGContextAddArc(context, center.x, center.y, radius + 4, startAngle, endAngle, 0); // create an arc the +4 just adds some pixels because of the polygon line thickness
CGContextStrokePath(context); // draw

// inscribed circle
float angle = M_PI - ((2 * M_PI) / polygon.numberOfSides); // need the polygon angles
CGContextSetLineWidth(context, 2); // set the line width
CGContextSetRGBStrokeColor(context, 20.0 / 255, 101.0 / 255.0, 211.0 / 255.0, 1.0);
CGFloat innerradius = (0.9 * center.x) * sin(angle / 2); // calc the inner radius
CGContextAddArc(context, center.x, center.y, innerradius - 3, startAngle, endAngle, 0); // create an arc the minus 3 subtracts some pixels because of the polygon line thickness
CGContextStrokePath(context); // draw