Question

What is the value of x in the following diagram

Answer 1

The value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

What is the property of perpendicular on chord in circle?

The line which is drawn from the center of the circle perpendicular to  the chord in the circle bisect the chord into two equal shape.

In the given, diagram the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8.

These both the lines are equal in length as both are drawn from the center of the circle and has a perpendicular bisector for the 15 units length chord in the circle. Thus,

$3x+1=x+8\\3x-x=8-1\\2x=7\\x=\dfrac{7}{2}\\x=3.5$

Thus, the value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

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