Two circles k1 and k2, have a common chord. The chord is a side of the inscribed square of the circle k1 and is also a side of the inscribed regular hexagon of the circle k2. What is the ratio of the circles' radii?
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Solution :-
Let us assume that,
- Length of common chord is a unit .
- Radius of circle with inscribe square = r unit.
- Radius of circle with inscribe regular hexagon = R unit.
we know that,
- Diagonal of square = Diameter of circle . { when a square is inscribed in the circle . }
- Diagonal of square = √2 * side .
so,
→ √2a = 2r
→ r = (√2a/2) unit .
we also know that, when a regular hexagon is inscribed in a circle ,
- Radius of circle = Side of regular hexagon .
so,
→ R = a unit .
therefore,
→ r : R = (√2a/2) : a
→ r : R = (√2/2) : 1
→ r : R = √2 : 2 (Ans.)
{ Excellent Question. }
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