Represent on the number line.

Step 1: Draw a line segment of 9.3 unit. Then, extend it to C so that BC = 1 unit.

Step 2: Now, AC = 10.3 units. Find the center of AC and mark it as O

Step 3: Draw a semi-circle with radius OC and center O

Step 4: Draw a perpendicular line BD to AC at point B intersecting the semi-circle at D. And then, join OD

Step 5: Now, OBD is a right angled triangle

Here, OD = 10.3/2 (Radius of semi-circle)

OC = 10.3/2

BC = 1

OB = OC – BC

= (10.3/2 - 1)

= 8.3/2

Using Pythagoras theorem,

OD^{2} = BD^{2} + OB^{2}

()^{2} = BD^{2} + ()^{2}

BD^{2} = ()^{2} - ()^{2}

BD^{2} = ( – ) ( + )

BD^{2} = 9.3

BD=

Thus, the length of BD is

Step 6: Taking BD as radius and B as the center, construct an arc which touches the line segment.

Now, the point where it touches the line segment is at a distance of from O as shown in the figure below

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