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Let ABC be a triangle in which the line joining the circumecentre and incentre is parallel to base BC of the triangle. Then answer the following questions : If ODEI is a square where O and I stands for circumcentre and incentre, respectively and D and E are the point of perpendicular from O and I on the base BC, then |
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Answer» `(r )/(R )=(3)/(8)` Now, `OI = sqrt(R^(2)-2Rr)` `therefore sqrt(R^(2)-2Rr) = R cos A` `RARR R^(2)-2Rr = R^(2)cos^(2)A` or `1-cos^(2)A=(2R)/(R )` Also `cos A = (r )/(R )` `rArr 1-((r )/(R ))^(2)=(2r)/(R )` `rArr ((r )/(R ))^(2)+(2r)/(R )-1=0` `rArr (r )/(R )= sqrt(2)-1` |
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