1. 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.)
2. 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).
3. 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.)
4. 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.)
5. Draw a triangle whose two sides are 7 cm and 6 cm, and the included angle is 75°. Then draw the incircle of the triangle.
6. 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.)
7. 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.)
8. 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.)
9. 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.)
10. 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)
11. 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).
12. 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).
13. 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.)
14. 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.)
15. Draw a triangle whose sides are 7 cm, 6 cm, and 5.5 cm respectively. Draw the incircle of the triangle. (Only provide the diagram)
16. 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).
17. 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.
18. Draw triangle ABC where AB = 8 cm, BC = 6 cm, and ∠ABC = 60°. Construct the circumcircle of that triangle. (Only construction marks are required).
19. 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.
20. 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.
21. The perimeters of two similar triangles are 27 cm and 16 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.
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. “The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of one side of the first triangle is 9 cm, what is the length of the corresponding side of the second triangle.”
24. 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.)
25. 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.)
26. 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.
27. “The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of one side of the first triangle is 9 cm, calculate the length of the corresponding side of the second triangle.”
28. Draw a right-angled triangle where the two sides adjacent to the right angle are 5 cm and 6 cm. Then, draw an incircle (a circle inscribed inside the triangle) within that triangle.
29. Draw a right-angled triangle in which the two sides adjacent to the right angle are 5 cm and 6 cm. Then draw a square that has the same area as that triangle.
30. 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.
