In a circle, diameter AB¯¯¯¯¯¯¯¯ is perpendicular to chord CD¯¯¯¯¯¯¯¯ at point L. Which statement will always be true about this circle?

CL = LD

Step-by-step explanation:

In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?

1) (CL)(LD)=AB

2) AL > LB

3) CL = LD

4) BL > AB

The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L.

Since CD is bisected at point L, CL = LD

Also CD = 2CL = 2LD

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it