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  • 17-04-2020
  • Mathematics
contestada

Given that BE=6, CE=6,
and FE measures 5 more
than DE, find the length
of DE.​

Given that BE6 CE6and FE measures 5 morethan DE find the lengthof DE class=

Respuesta :

PollyP52 PollyP52
  • 17-04-2020

Answer:

DE = 4 units.

Step-by-step explanation:

By the chord intersection theorem:

BE * CE = DE * FE

But FE = DE + 5 so:

BE * CE = DE * (DE + 5)

6 * 6 = DE^2 + 5DE

DE^2 + 5DE  - 36 = 0

(DE + 9)(DE - 4) = 0

So DE = -9 or 4

It can't be negative so DE = 4.

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