Using ruler compasses only, construct \vartriangle ABC in which BC=7.5cm, \angle ABC={{60}^{\circ }}and AC-AB=1.5cm. Inscribe a circle in the \vartriangle ABC and measure its radius.
Using ruler compasses only, construct \vartriangle ABC in which BC=7.5cm, \angle ABC={{60}^{\circ }}and AC-AB=1.5cm. Inscribe a circle in the \vartriangle ABC and measure its radius.

In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length.

In math, the circumference is the edge of a circle or oval.

A digression (tangent) to a circle is a straight line which contacts the circle at just one point.

A perpendicular bisector of a line section is a line fragment opposite to and going through the midpoint of (left figure).

As per the dimensions given in the question, circle to circumcircle of ΔABC is constructed.

Steps for constructions:

1. First draw a lineBC=7.5cm using a ruler.

2. Draw an arc making an angle of {{60}^{\circ }}with BC, at B.

3. Then on the arc cut AC=AB+1.5cm=7.5+1.5=9cm cutting the previous arc

4. Now join AC and AB.

5. Then construct an angle bisector of \angle Aand\angle B, which meet at O.

6. Draw a perpendicular to BC from O and mark it as P.

6. OP as radius make a circle touching all three sides of the triangle.

7. Therefore, above circle is the required circle with radius of2.3cm.