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If Delta(1) is the area of the triangle ...

If `Delta_(1)` is the area of the triangle with vertices `(0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2)` is the area of the triangle with vertices `(a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha)` and `Delta_(3)` is the area of the triangle with vertices `(0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha)`. Show that there is no value of `alpha` for which `Delta_(1), Delta_(2)` and `Delta_(3)` are in GP.

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