Handledning – Cevianer
Förkunskaper: Inget utöver vanlig geometri (arean av trianglar) krävs. Ma1.
Syfte: Träna upp färdigheten att med enkla geometriska medel visa ett samband (en intrssant formel).
Lösningsförslag inkl. elevtips
![\[\frac{\left| area (APB)\right| }{\left| area (APC)\right| }=\frac{½h\left\vert BD\right\vert }{½h\left\vert DC\right\vert }=\frac{\left\vert BD\right\vert }{\left\vert DC\right\vert }.\]](http://mattesherpa.se/wp-content/ql-cache/quicklatex.com-8fa187f27a9f02868285a5e37709252d_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{\left| area (ABD)\right| }{\left| area (ADC)\right| }=\frac{½h'\left\vert BD\right\vert }{½h'\left\vert DC\right\vert }=\frac{\left\vert BD\right\vert }{\left\vert DC\right\vert }\]](http://mattesherpa.se/wp-content/ql-cache/quicklatex.com-8a1f9f1f97bb47551c93f6aa737a4911_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{\left| area (APB)\right| }{\left\vert area (APC)\right\vert }=\frac{\left\vert area (APD)-area(PBD)\right\vert }{\left\vert area (APC)-area(PDC)\right\vert }=\frac{\left\vert BD\right\vert }{\left\vert DC\right\vert }.\]](http://mattesherpa.se/wp-content/ql-cache/quicklatex.com-0fb1d24ea9aa6c5448e1119db9f0564d_l3.png "Rendered by QuickLaTeX.com")
![\[\left[ \frac{x}{y}=\frac{c}{d} \Longrightarrow \frac{x}{y}=\frac{x-c}{y-d}, \,\, y \neq d\right]\]](http://mattesherpa.se/wp-content/ql-cache/quicklatex.com-54f6a9d27cd5ad156dfc3ab3617273e3_l3.png "Rendered by QuickLaTeX.com")
Nästa steg: Visa nu uppgiften Cevas Sats
Av Samuel Bengmark
