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Question Number 217783 by malwan last updated on 21/Mar/25

$$ \\ $$

Commented by malwan last updated on 21/Mar/25

$$ \\ $$

Commented by malwan last updated on 21/Mar/25

I cant send a photo

$${I}\:{cant}\:{send}\:{a}\:{photo}\: \\ $$

Commented by mr W last updated on 21/Mar/25

you seem still to have the old  problem.

$${you}\:{seem}\:{still}\:{to}\:{have}\:{the}\:{old} \\ $$$${problem}. \\ $$

Commented by Tinku Tara last updated on 21/Mar/25

Maybe your image is too big.  Try uploading a smaller image

$$\mathrm{Maybe}\:\mathrm{your}\:\mathrm{image}\:\mathrm{is}\:\mathrm{too}\:\mathrm{big}. \\ $$$$\mathrm{Try}\:\mathrm{uploading}\:\mathrm{a}\:\mathrm{smaller}\:\mathrm{image} \\ $$

Commented by malwan last updated on 22/Mar/25

I will try sir

$${I}\:{will}\:{try}\:{sir} \\ $$

Commented by malwan last updated on 22/Mar/25

Commented by malwan last updated on 22/Mar/25

That was my question

$${That}\:{was}\:{my}\:{question}\: \\ $$

Commented by mr W last updated on 23/Mar/25

only if it is also given that PX⊥XY.

$${only}\:{if}\:{it}\:{is}\:{also}\:{given}\:{that}\:{PX}\bot{XY}. \\ $$

Commented by mr W last updated on 23/Mar/25

Commented by mr W last updated on 23/Mar/25

tan α=((XY)/(XP))=((2r)/r)=2  ⇒α=tan^(−1) 2  β=(π/2)−α=(π/2)−tan^(−1) 2  ∠PXQ=2β=2((π/2)−tan^(−1) 2)=π−2 tan^(−1) 2

$$\mathrm{tan}\:\alpha=\frac{{XY}}{{XP}}=\frac{\mathrm{2}{r}}{{r}}=\mathrm{2} \\ $$$$\Rightarrow\alpha=\mathrm{tan}^{−\mathrm{1}} \mathrm{2} \\ $$$$\beta=\frac{\pi}{\mathrm{2}}−\alpha=\frac{\pi}{\mathrm{2}}−\mathrm{tan}^{−\mathrm{1}} \mathrm{2} \\ $$$$\angle{PXQ}=\mathrm{2}\beta=\mathrm{2}\left(\frac{\pi}{\mathrm{2}}−\mathrm{tan}^{−\mathrm{1}} \mathrm{2}\right)=\pi−\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \mathrm{2} \\ $$

Commented by malwan last updated on 23/Mar/25

fantastic ,  thank you so much sir

$${fantastic}\:, \\ $$$${thank}\:{you}\:{so}\:{much}\:{sir}\: \\ $$

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