AQ, AR, BC are tangents for the circle with centre O and BC, AD, AE are tangents to the circle with centre O\'. Prove that ABO\'C is parallelogram. It is given that radius of bigger circle is three times the smaller circle.

Asked by Lalit Kariya | 3rd Mar, 2012, 01:15: PM

Expert Answer:

In triangle AOQ and AO'D the sides are in ratios as the triangles are similar
so AO/AO' = AQ/AD = OQ/O'D
On Solving we get , AO = 2r
Now , If BC is tangent at point E the AE = AO + OE = 3r = O'E
Also , BE = CE
Thus diagonals AO' and BC are bisected at point E
Hence , ABO'C is a parallelogram

Answered by  | 6th Mar, 2012, 03:05: PM

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