Question

Solve this for me (geometry)

Answer 1

Given:

A figure of a circle.
`KJ=6,KL=x-2,ML=4`.

To find:

The length of KJ.

Solution:

From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.

Therefore, the length of KJ is 6 units.

Note: In the given question we need to find KL instead of KJ because KJ is already given.

According to the tangent secant theorem:

`a^2=bc`

Where,

• a is the length of the tangent.
• b is the length of the external segment of the secant.
• c is the measure of the secant.

Using the tangent secant theorem, we get

`ML^2=KL* JL`

`(4)^2=(x-2)* (6+x-2)`

`16=(x-2)* (4+x)`

`16=4x+x^2-8-2x`

On further simplification, we get

`16=x^2+2x-8`

`0=x^2+2x-8-16`

`0=x^2+2x-24`

Splitting the middle term, we get

`x^2+6x-4x-24=0`

`x(x+6)-4(x+6)=0`

`(x+6)(x-4)=0`

`x=-6,4`

For
`x=-6`,

`KJ=-6-2`

`KJ=-8`, which is not possible because side cannot be negative.

For
`x=4`,

`KJ=4-2`

`KJ=2`

Therefore, the measure of KL is 2 units.