Let ABC be an equilateral triangle and let D be an inner point of the side BC. A circle is tangent to BC at D and intersects the sides AB and AC in the inner points M,N and P,Q respectively. Prove that ∣BD∣+∣AM∣+∣AN∣=∣CD∣+∣AP∣+∣AQ∣. geometryEquilateralcircle