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This was part of the solution of a question.

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But the part of the explanation says that:

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I don't understand how it works. Could anyone explain why $AC={CP\cdot QU \over UP}$ ?

I think I can carry it on once I understand this.

1 Answers 1

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Hint: Similar triangle. Try to show \begin{align} \Delta PQU \sim \Delta PAC. \end{align}

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    Is it still similar even though $\triangle PQU$'s hypotenuse is the part of triangle's height, and hypotenuse of $\triangle PAC$ is the slant of the triangle? – 2017-02-06
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    Look carefully at the correspondence. $A$ is corresponding to $Q$. – 2017-02-06
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    ${AC \over CP} = {QU \over UP}$. I mean is it still similar even if their hypotenuses are not on the same line? – 2017-02-06
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    I don't quite understand what you mean. – 2017-02-06