Anoara drew a triangle ABC in her exercise book. We bisect side BC by compass and then the median AD. I trisect AD in AE, EF and FD. Now we join B and F by scale and extended it to X such that it intersect AC at X.

Measuring by scale we see,

AX= CX(Let’s put the number)

Step1: Draw a ΔABC of any length with scale

Now we will bisect BC and mark the centre as D

Step2: Take any distance in compass approximately greater than half of BC. Keep the needle of compass on point B and mark arcs above and below BC

Step3: Keeping the distance in compass same as that of in step2 keep the needle of compass on point C and intersect arcs drawn in step2. Join there intersection points. Mark the intersection of line with BC as D and join AD. AD is the median

Now we have to trisect the median AD that is we have to divide the median in 3 equal parts

The first step when dividing a line in equal parts we draw a ray at any angle to the given line

Here the line which we have to divide is AD. Let AB be the ray

Step4: Take any distance in compass and keep the needle of compass on point A and draw an arc intersecting AB. Name the intersection point as X₁. keeping the distance same in compass keep the needle on point X₁ and mark an arc intersecting AB at X₂. Draw 3 such parts that is upto X_3. By doing this we are making 3 equal parts on the AB

Step5: Join X₃ and D and draw parallels to DX₃ from X₂ and X₁ which intersects AD at F and E respectively.

Thus we have divided AD in 3 equal parts AE, EF and FD

Step6: Draw a line passing through points B and F and let it intersect AC at X

Measure AX and XC using scale both are equal

AX = CX

Hence the box should be filled with 1

⇒ AX = 1 × CX