tangent.c

#include<stdio.h>
#include<assert.h>
#include<math.h>

float ax = 4.5f, ay = 5.5f;
float r = 2.0f;
float ox = -3.4f, oy = -5.4f;

int main()
{
	float l = sqrtf((ax - ox) * (ax - ox) + (ay - oy) * (ay - oy)); 

	assert(l > r);

	float sin_theta = r / l;
	float cos_theta = sqrtf(1.f - sin_theta * sin_theta);

	// sin_theta = - sin_theta;

	float _ox = ax + cos_theta * (ox - ax) + sin_theta * (oy - ay);
	float _oy = ay - sin_theta * (ox - ax) + cos_theta * (oy - ay);

	float lap = sqrtf(l * l - r * r);

	float px = ax + (_ox - ax) * lap / l;
	float py = ay + (_oy - ay) * lap / l;

	printf("%f %f\n", px, py);
}