1. I draw a square having the same area as that of an equilateral triangle with each side measuring 7 cm.
2. Draw an equilateral triangle ABC with each side measuring 5 cm. Then, draw the circumcircle of that triangle. At point A on the circle, draw a tangent. On the tangent, take a point P such that AP = 5 cm. From point P, draw another tangent to the circle, and write down which point on the circle this second tangent touches.
3. Draw an isosceles triangle whose base is 7.8 cm and the length of each of the equal sides is 6.5 cm. Then draw an incircle (an inscribed circle) inside that triangle.
4. Draw a triangle with three sides measuring 7 cm, 6 cm, and 5.5 cm. Then, draw an incircle for that triangle.
5. Construct a right-angled triangle in which the two arms adjacent to the right angle are 7 cm and 9 cm. Draw an incircle (inscribed circle) of that triangle and measure its radius. (Each construction step must be marked.)
6. Draw an equilateral triangle with side length 7 cm. Then draw both the circumcircle and the incircle of the triangle. Using a scale, determine the lengths of the circumradius and the inradius. Also, write whether there is any relationship between them.
7. Draw an isosceles triangle with a base of 6.5 cm and two equal sides of 7 cm each. Then, draw the incircle of that triangle.
8. Draw an isosceles triangle with a base length of 5.2 cm and each of the equal sides measuring 7 cm. Then, construct the circumcircle of the triangle and measure the circumradius. (Only mark the construction steps).
9. Draw a right-angled triangle with its adjacent sides measuring 7 cm and 9 cm. Then, draw an incircle for the triangle. (Provide only the construction steps.)
10. Draw a triangle with side lengths of 5 cm, 6 cm, and 7 cm. Then, draw the incircle of that triangle (only construction marks should be included).
11. Draw a triangle with two sides measuring 6.5 cm and 5.7 cm, and the included angle. Then, draw the incircle of the triangle.
12. An isosceles triangle where the base is 7.8 cm and each of the equal sides is 6.5 cm. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).
13. Draw an equilateral triangle ABC with each side measuring 5 cm. Then, draw the circumcircle of \(\triangle\)ABC. At points A, B, and C on the circle, draw tangents.
14. Draw an isosceles triangle in which each of the equal sides is 7 cm and the base is 8 cm long. Then, draw an incircle of that triangle.
15. Draw a triangle with side lengths of 4.5 cm, 5.5 cm, and 6 cm. Draw the incircle of that triangle.
16. Draw a right-angled triangle with both perpendicular sides measuring 4 cm. Then draw the incircle of the triangle. (Only include the construction markings.)
17. Draw a triangle with sides of 6 cm, 8 cm, and 10 cm. Then draw the incircle of that triangle.
18. Draw a right-angled triangle whose two sides adjacent to the right angle are 7 cm and 9 cm respectively. Then draw the incircle of that triangle. (Only construction marks are required.)
19. Draw a triangle in which two sides are 9 cm and 7 cm, and the included angle between them is 60°. Then draw the incircle of that triangle. (Only construction marks are required.)
20. Draw the incircle of an equilateral triangle with side length 10 cm. (Only construction marks are required.)
21. Draw a right-angled triangle whose two sides adjacent to the right angle are 4.5 cm and 6 cm. Then draw the incircle of that triangle. (Only construction marks are required.)
22. Draw a triangle with two sides measuring 7.6 cm and 6 cm, and an included angle of 75\(^o\). Then, construct its incircle.
23. Draw an equilateral triangle with a side length of 6 cm and then inscribe its incircle. (Only construction marks should be shown in each step.)
24. Draw a triangle with side lengths of 7 cm, 6 cm, and 5.5 cm. Draw the incircle of the triangle and measure the radius of the incircle.
25. Draw an isosceles triangle where the base length is 5 cm and each of the equal sides is 6 cm. Then, draw the incircle of the triangle. (Only construction marks should be indicated in each case.)
26. Here is the drawing of an isosceles triangle with a base length of 5.6 cm and equal sides of 7.5 cm each, along with its incircle.
27. Draw a square with the same area as an equilateral triangle with a side length of 7 cm.
28. Draw a right-angled triangle with the two sides adjacent to the right angle measuring 4 cm each. Then draw the circumcircle of the triangle. (Only construction marks are required.)
29. The length of one side is 6.2 cm, and the measures of the two angles adjacent to that side are 50° and 75°. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).
30. A right-angled triangle in which the two sides adjacent to the right angle are 7 cm and 9 cm. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).
