Lines Parallel to the Sides of a Triangle

PP'

≈

0.57

QQ'

≈

0.47

RR'

≈

0.51

AB

≈

1.02

BC

≈

0.86

AC

≈

1.27

1

PP'

+

1

QQ'

+

1

RR'

≈

5.88

2

(

1

AB

+

1

BC

+

1

AC

)

≈

5.88

Let ABC be a triangle and let the angle bisectors at A, B, and C intersect the opposite sides at points P, Q, and R. Draw lines from P, Q, and R parallel to AB, BC, and AC that intersect AC, AB, and BC at P', Q', and R'. Then

1

PP'

+

1

QQ'

+

1

RR'

=2

1

AB

+

1

BC

+

1

AC

.

Drag the points A, B, or C to change the figure.