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.

Perpendicularprojected fromcenterof acircleto itschord bisectsit. The value of the x for this case is: x = 1.565 ft approximately.## What is Pythagoras Theorem?

If ABC is a

trianglewith AC as thehypotenuseandangleB with 90 degrees then we have:where |AB| =

lengthof line segment AB. (AB and BC are rest of the two sides of thattriangleABC, AC being thehypotenuse).## What is the relation between line perpendicular to chord from the center of circle?

If the considered circle has

centerO andchordAB, then if there isperpendicularfrom O to AB at point C, then that point C isbisecting(dividing in two equal parts) theline segmentAB.Or |AC| = |CB|

For this case, consider the

diagrambelow.The line OC

dividesAB inhalf.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

triangleOBC contains a right angle, we can usePythagoras theorem, and therefore, we get:(took positive root as 'x' represents

measurementoflength, which is a non-negativequantity).Thus, the value of the x for this case is: x = 1.565 ft approximately.

Learn more about

Pythagoras theoremhere:https://brainacademy.pro/question/12105522

Learn more about

chordof acirclehere:https://brainacademy.pro/question/13046585

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