Find a tangent point on circle?

Question

Given a line with first end point P(x1,y1) another end point is unknown, intersect with a circle that located at origin with radius R at only one point(tangent) T(x2,y2). An

Answer 1

imbrizi's answer assumes that the circle's center is (0,0).

This is the correct answer in Objective C:

- (NSArray *)pointsTangentToCircleWithCenter:(CGPoint)centerPoint
                                      radius:(CGFloat)radius
                                  outerPoint:(CGPoint)outerPoint {

    float dx = centerPoint.x - outerPoint.x;
    float dy = centerPoint.y - outerPoint.y;
    float dd = sqrt(dx*dx + dy*dy);
    float a = asinf(radius / dd);
    float b = atan2f(dy, dx);
    float t1 = b - a;
    CGPoint tangentPoint1 = CGPointMake(centerPoint.x + radius*sinf(t1), 
                                        centerPoint.y + radius*-cosf(t1));

    float t2 = b + a;
    CGPoint tangentPoint2 = CGPointMake(centerPoint.x + radius*-sinf(t2), 
                                        centerPoint.y + radius*cosf(t2));

    NSArray *points = @[
                        [NSValue valueWithCGPoint:tangentPoint1],
                        [NSValue valueWithCGPoint:tangentPoint2]
                        ];
    return points;
}