Index: lib/geo/area.cpp
==================================================================
--- lib/geo/area.cpp
+++ lib/geo/area.cpp
@@ -5,14 +5,11 @@
 // Verified by
 //   - SRM 337 Div1 LV3
 //   - SRM 486 Div1 LV3
 //-------------------------------------------------------------
 
-double outer_prod( pt a, pt b )
-{
-	return (a.real()*b.imag() - b.real()*a.imag())/2;
-}
+double outer_prod(const CMP& a, const CMP& b) { return imag(conj(a)*b); }
 
 double area( const vector<pt>& q )
 {
 	double a = 0.0;
 

ADDED   lib/geo/circle.cpp
Index: lib/geo/circle.cpp
==================================================================
--- lib/geo/circle.cpp
+++ lib/geo/circle.cpp
@@ -0,0 +1,36 @@
+// Verified: partly by geocon2013 D(1).
+
+// Crosspoing of a line (not lineseg!) and a circle).
+bool line_circle(CMP la, CMP lb, CMP c, double r, CMP* p1, CMP* p2)
+{
+	CMP v = (lb-la) / abs(lb-la);
+	CMP o = (c-la) / v;
+	if( abs(o.imag()) > r )
+		return false;
+	double dx = sqrt(r*r - o.imag()*o.imag());
+	*p1 = la + (o.real()-dx)*v;
+	*p2 = la + (o.real()+dx)*v;
+	return true;
+}
+
+// Whether or not |p| is in the circle (c, r).
+bool pt_in_circle(CMP p, CMP c, double r)
+{
+	return norm(p-c) <= r*r;
+}
+
+// Assuming |o| is outside (C,r), compute the two tangent points.
+void sessen(CMP o, CMP c, double r, CMP* p1, CMP* p2)
+{
+	double len = sqrt(norm(c-o) - r*r);
+	double theta = asin(r/abs(c-o));
+
+	if(p1) *p1 = o+(c-o)*polar(len/abs(c-o), theta);
+	if(p2) *p2 = o+(c-o)*polar(len/abs(c-o), -theta);
+}
+
+// For two points |p| and |q| on (c,r), compute their distance along the circle.
+double d_on_c(CMP c, double r, CMP p, CMP q)
+{
+	return abs(arg((p-c) / (q-c))) * r;
+}

DELETED lib/geo/line_circle.cpp
Index: lib/geo/line_circle.cpp
==================================================================
--- lib/geo/line_circle.cpp
+++ lib/geo/line_circle.cpp
@@ -1,14 +0,0 @@
-typedef long double LD;
-typedef complex<LD> CMP;
-
-bool line_circle(CMP la, CMP lb, CMP c, LD r, CMP* p1, CMP* p2)
-{
-	CMP v = (lb-la) / abs(lb-la);
-	CMP o = (c-la) / v;
-	if( abs(o.imag()) > r )
-		return false;
-	LD dx = sqrt(r*r - o.imag()*o.imag());
-	*p1 = la + (o.real()-dx)*v;
-	*p2 = la + (o.real()+dx)*v;
-	return true;
-}

Index: lib/geo/pt_in_poly.cpp
==================================================================
--- lib/geo/pt_in_poly.cpp
+++ lib/geo/pt_in_poly.cpp
@@ -4,14 +4,11 @@
 //
 // Verified by
 //   - AOJ 0012 (only triangles)
 //-------------------------------------------------------------
 
-double outer_prod( CMP a, CMP b )
-{
-	return (a.real()*b.imag() - b.real()*a.imag())/2;
-}
+double outer_prod(const CMP& a, const CMP& b) { return imag(conj(a)*b); }
 
 bool point_in_polygon( vector<CMP>& ps, CMP p )
 {
 	bool in = false;
 	for(int i=0; i<ps.size(); ++i) {