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Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.

Answer:

**Solution:**

An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

Steps to construct:

Step 1: Draw a line segment BC = 5cm.

Step 2: With Center as B and radius 5cm, with center as C and radius 5cm draw two arcs which intersect each other at point A.

Step 3: Join AB and AC.

Step 4: Draw the angle bisector of angles B and C which intersects each other at point I.

Step 5: From I, draw a perpendicular ID on BC.

Step 6: With center as I and radius ID, draw a circle which touches the sides of the triangle internally.

Step 7: On measuring the radius ID = 1.5cm (approx).

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