Show that a triangle is right-angled if the sides are $a={{m}^{2}}-{{n}^{2}}$, $b=2mn$ and \(c={

Question

Show that a triangle is right-angled if the sides are $a={{m}^{2}}-{{n}^{2}}$, $b=2mn$ and $c={{m}^{2}}+{{n}^{2}}$ where $m$ and $n$ are positive, and $m>n$. In triangle $ABC$, $AB=AC$,$P$ is an arbitrary point on $BC$. Show that $A{{B}^{2}}-A{{P}^{2}}=PB\times PC$.

Accepted Answer

(a) $c^2=a^2+b^2$, so the triangle is right-angled opposite $c$ (b) $AB^2-AP^2=PB\times PC$

IP1U13 SWII (Pythagoras) Q8

IP1U13 SWII (Pythagoras) Q8

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