<A=45^o, CD \perp AB, P\perp BC iff |AP| = |BC|.

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<A=45^o, CD \perp AB, P\perp BC iff |AP| = |BC|.

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#1 h Aug 4, 2019, 11:02 PM • 1 Y

Y by Adventure10

Let $ABC$ be an acute triangle such that $\angle BAC = 45^o$ . Let $D$ a point on $AB$ such that $CD \perp AB$ . Let $P$ be an internal point of the segment $CD$ . Prove that $AP\perp BC$ if and only if $|AP| = |BC|$ .

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#2 h Aug 4, 2019, 11:10 PM • 1 Y

Y by Adventure10

Refer here. Let $P$ $\in$ $CD$ , such $AP \perp BC$ $\implies$ $AP=2R \cos A$ $=$ $\sqrt{2}a \cdot \frac{1}{\sqrt{2}}$ $=$ $a$ . The iff part follows from phantom points

This post has been edited 3 times. Last edited by AlastorMoody, Aug 4, 2019, 11:38 PM

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