Answer: The value of x is 2 units.
Explanation:
Since we have given that
AB and CD are two chords that are intersected externally at point E.
As we know the relation regarding the above i.e.
[tex]EA\times EB=EC\times ED[/tex]
Here,
EB=x+1
EA=x+1+11 = (x+12)
EC=x+4
ED=x+4+1 = (x+5)
Now, we put the values in the relation given above :
[tex](x+1)(x+12)=(x+4)(x+5)\\\\x^2+13x+12=x^2+9x+20\\\\12+13x=20+9x\\\\13x-9x=20-12\\\\4x=8\\\\x=\frac{8}{4}=2\\\\x=2\ units[/tex]
Hence, the value of x is 2 units.
Answer:
x = 2 is the answer.
Step-by-step explanation:
When two chords AE and ED are drawn from an external point E to a circle then by theorem we know the relation
AE×BE = DE×CE
AE = x + 1 + 11 = x + 12
BE = x + 1
CE = x + 4
DE = x + 4 + 1 = x + 5
Now putting these values in the formula
(x + 12)(x + 1) = (x + 4)(x + 5)
x² + 12x + x + 12 = x² + 5x + 4x + 20
13x + 12 = 9x + 20
13x - 9x = 20 - 12
4x = 8
x = 2
x = 2 is the answer.
