1. Draw an equilateral triangle with side length 6 cm and then draw its incircle. (Only construction marks are required.)
2. Draw an equilateral triangle with side length 6 cm and construct its incircle. (Only drawing symbols are required)
3. 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.)
4. Draw the incircle of an equilateral triangle with side length 10 cm. (Only construction marks are required.)
5. Draw an equilateral triangle with a side length of 7 cm and construct its incircle. (Mark all construction steps.)
6. 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.)
7. Draw a rectangle with sides of 8 cm and 6 cm, and then draw a square having the same area as that rectangle. (Only construction marks are required.)
8. Draw a right-angled triangle whose hypotenuse is 10 cm and one of the other sides is 6.5 cm. Then, draw the incircle of this triangle. (Only construction marks are required.)
9. 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.)
10. Draw a triangle with a base length of 6.2 cm and the two adjacent angles measuring 50° and 75°; then construct its incircle. (Only provide the construction marks.)
11. 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).
12. Draw a triangle where one side is 6.7 cm and the two adjacent angles are 75° and 55°. — Draw the triangle and then draw its circumcircle. Mark the position of the circumcenter and measure and write the length of the circumradius (i.e., the radius of the circumcircle). [Only drawing symbols required]
13. Draw triangle ABC in which BC = 7 cm, AB = 5 cm, and AC = 6 cm. Then construct the incircle of the triangle. (Only the construction markings are required.)
14. If a triangle similar to one with sides 4 cm, 6 cm, and 8 cm has its largest side measuring 6 cm, what is the length of the smallest side of that triangle?
(a) 4 cm (b) 3 cm (c) 2 cm (d) 5 cm
15. 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.)
16. Draw a triangle ABC such that BC = 6 cm, CA = 5.5 cm, and AB = 4.5 cm. Then draw the incircle of ∆ABC. (Only construction marks are required.)
17. Draw triangle ABC such that BC = 7 cm, AB = 5 cm, and AC = 6 cm. Then draw the circumcircle of triangle ABC. (Only construction marks are required.)
18. Draw a rectangle with a length of 7 cm and a width of 4 cm; now draw a square with the same area as that rectangle. (Only the construction marks are required.)
19. Draw a right-angled triangle whose hypotenuse is 9 cm and one of the other sides is 5.5 cm. Then draw an incircle of the triangle. (Only the construction marks are required.)
20. Draw a right-angled triangle whose two sides adjacent to the right angle are 8 cm and 6 cm respectively, and draw an incircle of the triangle. (Only construction marks are required)
21. In a circle with a radius of 5 cm, AB and AC are two equal chords. The center of the circle is located outside the triangle ABC. If AB = AC = 6 cm, determine the length of the chord BC.
22. 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).
23. Draw a triangle with two sides measuring 7.6 cm and 6 cm, and an included angle of 75\(^o\). Then, construct its incircle.
24. 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.)
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 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.)
28. In a circle with a radius of 5 cm, AB and AC are two equal-length chords. The center of the circle lies outside triangle ABC. Given AB = AC = 6 cm, find the length of chord BC.
29. An equilateral triangle where each side is 6 cm. — Draw the triangle and then draw its circumcircle. Mark the position of the circumcenter and measure and write the radius of the circumcircle. [Only drawing symbols required]
30. The lengths of two sides are 7.6 cm and 6 cm, and the included angle between them is 75°. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).
