Question

What is the value of x?



x =

Answer 1

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.

Answer 2

Answer: The value of x is 2 units.

Step-by-step 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.

`EA* EB=EC* ED`

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 :

`(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=(8)/(4)=2\\\\x=2\ units`

Hence, the value of x is 2 units.