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 points. Now, you should have an acute triangle: ABC.

Step 2

BisectB.

Using a compass, draw a relatively small circle at pointB.

Mark the intersections of circleB

with the sides ofB,

and label themP

andQ.

Step 3

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

and another at pointQ.

Mark the intersection of P

and Q

that is in the interior ofABC and label this pointR.

Step 4

Using a straightedge, draw a line through pointsB

andR.

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

Step 5

BisectC.

Using a compass, draw a relatively small circle at pointC.

Mark the intersections of circleC

with the sides ofC,

and label themU

andV.

Step 6

Keep the compass setting and draw two circles one centered at pointU

and another at pointV.

Mark the intersection of U

andV

that is in the interior ofABC,

and label this pointT.

Step 7

Using a straightedge, draw a line through pointsC

andT.

Make sure this line intersectsBR. Mark this intersection as pointX.

Step 8

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

Using a compass, construct a circle at pointB

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

with a radius of CX. Mark their intersection as pointZ.

Step 9

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

Step 10

Using a compass, draw a circle with a radius ofXY at pointX.

Mark the intersections of circleX

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

Name the other two pointsF

andL.