Question Number 101937 by 1549442205 last updated on 06/Jul/20

Given a circle with the center at the point O and the radius of the length R.From a point A outside so that AO=2R,drawing two tangents AB and AC to the circle (B and C are the tangency points).Take a arbitrary point M on smaller arc BC (M differ from B and C) The tangent pass M cuts AB and AC at Pand Q respectively.The segments OP and OQ cuts BC at D and E respectively. i)Prove that PQ=2DE ii)Define the position of M such the area of the triangle ODE is smallest and expression it by R