Question

The altitudes AD and BE of triangle ABC intersect each other at O.
Prove that CD/AC = CE/BC.​

Answer 1

Given : The altitudes AD and BE of triangle ABC intersect each other at O.

To Prove : CD/AC = CE/BC

Proof : In ∆ADC and ∆BCE,

→ ∠ADC = ∠BEC [Each 90°]

→ ∠C = ∠C [Comman]

Hence by AA-criteria ∆ADC ~ ∆BCE.

Hence by Thales theorem,

→ CD/CE = AC/BC

By cross multiplication we get

→ CD/AC = CE/BC

Q.E.D