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