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

$ML^2=KL\times JL$

$(4)^2=(x-2)\times (6+x-2)$

$16=(x-2)\times (4+x)$

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

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.