Which construction uses the compass for only one step in addition to drawing the circle itself?
a. an equilateral triangle inscribed in a circle
b. a square inscribed in a circle
c. a regular hexagon inscribed in a circle
d. a diameter of a circle

Option D is correct.

Step-by-step explanation:

Given the constriction we have to choose the construction which uses the compass for only one step in addition to drawing the circle itself.

Option A: an equilateral triangle inscribed in a circle

Above construction uses three steps in addition to drawing the circle itself as equilateral triangle has 3 sides.

∴ not a correct option

Option B:  a square inscribed in a circle

Above construction uses 4 steps in addition to drawing the circle itself as square has 4 sides.

∴ not a correct option

Option C: a regular hexagon inscribed in a circle

Above construction uses 6 steps in addition to drawing the circle itself as regular hexagon  has 6 sides.

∴ not a correct option

Option D: a diameter of a circle

Above construction uses one step in addition to drawing the circle itself  

which is the correct option.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,