Find the value of x. Round to the nearest tenth. 1.4ft 2.1 ft 2x x = [ ? ]ft​ 5 (1 оценка)
4
astha8579 4 months ago
Светило науки - 824 ответа - 0 помощи

Perpendicular projected from center of a circle to its chord bisects it. The value of the x for this case is: x = 1.565 ft approximately.

### What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have: where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

### What is the relation between line perpendicular to chord from the center of circle?

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or |AC| = |CB|

For this case, consider the diagram below.

The line OC divides AB in half.

Since it is given that:
Length of AB = |AB| = 2x ft,

therefore, we get:
|AC| + |CB| = 2x

|AC|+|AC| = 2x (as |AC|=|CB|)

therfore, we get: |AC| = x feet = |CB|

Now,as the triangle OBC contains a right angle, we can use Pythagoras theorem, and therefore, we get: (took positive root as 'x' represents measurement of length, which is a non-negative quantity).

Thus, the value of the x for this case is: x = 1.565 ft approximately. 