Question

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

Answer 1

DE = 4 units.

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.