Step 1 Using a straightedge, draw an acute angle,B. Mark two points on either side ofB. Mark these pointsA andC. Use a straightedge to connect the...
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# Step 1Using a straightedge, draw an acute angle, ∠B. Mark two points on either side of ∠B.

Mark these points A

and C.

Use a straightedge to connect the points. Now, you should have an acute triangle: ABC.

Step 2

Bisect ∠B.

Using a compass, draw a relatively small circle at point B.

Mark the intersections of circle B

with the sides of ∠B,

and label them P

and Q.

Step 3

Keep the compass setting and draw two circles, one centered at point P

and another at point Q.

Mark the intersection of P

and Q

that is in the interior of ABC and label this point R.

Step 4

Using a straightedge, draw a line through points B

and R.

Make sure this line intersects the opposite side of the triangle, AC.

Step 5

Bisect ∠C.

Using a compass, draw a relatively small circle at point C.

Mark the intersections of circle C

with the sides of ∠C,

and label them U

and V.

Step 6

Keep the compass setting and draw two circles one centered at point U

and another at point V.

Mark the intersection of U

and V

that is in the interior of ABC,

and label this point T.

Step 7

Using a straightedge, draw a line through points C

and T.

Make sure this line intersects BR. Mark this intersection as point X.

Step 8

Construct a line that's perpendicular to BC  and goes through point X.

Using a compass, construct a circle at point B

with a radius of BX. Then use a compass to construct a circle at point C

with a radius of CX. Mark their intersection as point Z.

Step 9

Using a straightedge, draw XZ. Mark the intersection of XZ and BC as point Y.

Step 10

Using a compass, draw a circle with a radius of XY at point X.

Mark the intersections of circle X

and ABC. If you constructed this circle correctly, there will only be three points. One is already named Y.

Name the other two points F

and L.

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