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Construction of Incircle

In Δ ABC,if...

Question

In $Δ A B C, i f cot A = \sqrt{a c}, cot B = \sqrt{\frac{c}{a}}, cot C = \sqrt{\frac{a^{3}}{c}}$ (with usual notations),
then which of the following is/are correct

(a)

c = 1 - a - a^{2}

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(b)

c = 1 + a + a^{2}

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(c)

c = 1 - a + a^{2}

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(d)

c = a^{2} + a - 1

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A B C

cot A = \sqrt{a c}, cot B = \sqrt{\frac{c}{a}}, cot C = \sqrt{\frac{a^{3}}{c}}

C = a^{2} + a + 1

Δ A B C

A, B, C

\frac{a + c}{\sqrt{a^{2} - a c + c^{2}}} =

Δ A B C

A, B, C

\frac{a + c}{\sqrt{a^{2} - a c + c^{2}}} =

If a, b, c are in G.P., prove that:

(i) $a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

(ii) $a^{2} b^{2} c^{2} (\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}}) = a^{3} + b^{3} + c^{3}$

(iii) $\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{a + b + c}{a - b + c}$

(iv) $\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}} = \frac{1}{b^{2} - c^{2}}$

(v) $(a + 2 b + 2 c) (a - 2 b + 2 c) = a^{2} + 4 c^{2}$ .

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In ΔABC,ifcotA=√ac,cotB=√ca,cotC=√a3c (with usual notations),then which of the following is/are correct