4. Considere un círculo de radio $5$ y centro $O$ . Se trazan dos tangentes desde un punto exterior $C$ al círculo en los puntos $X$ y $Y$ de la circunferencia. $A$ y $B$ son puntos sobre $CX$ y $CY$ respectivamente tales que $AB$ es una tangente en $P$ . Si $CO = 13$ , halle el perímetro de $\triangle ABC$ . [asy] size(200); import graph; // Define center and radius pair O = (0,0); real r = 5; real d = 13; pair C = (d, 0); // Calculate tangent points X and Y mathematically real theta = acos(r/d); pair X = r * (cos(theta), sin(theta)); pair Y = r * (cos(theta), -sin(theta)); // Define P (tangency point for AB) - picking an angle between X and Y pair P = r * (cos(0.4), sin(0.4)); // Calculate points A and B where tangent at P hits CX and CY // This uses the formula for a tangent line at a point on a circle pair dirP = (cos(0.4), sin(0.4)); pair tanDir = (-sin(0.4), cos(0.4)); // A is intersection of line(C,X) and tangent at P pair A = extension(C, X, P, P + tanDir); // B is intersection of line(C,Y) and tangent at P pair B = extension(C, Y, P, P + tanDir); // Draw circle draw(circle(O, r), linewidth(0.8)); // Draw triangle and tangents draw(C--A--B--cycle, blue + linewidth(0.8)); draw(A--X, dashed); draw(B--Y, dashed); draw(O--X^^O--P, gray+dashed); // Labels dot("$O$", O, W); dot("$C$", C, E); dot("$X$", X, NW); dot("$Y$", Y, SW); dot("$A$", A, N); dot("$B$", B, S); dot("$P$", P, NE); label("$5$", O/2 + X/2, W); [/asy] Pi-Infinity