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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Subject: Geometry, Math
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