WBBSE Solutions For Class 10 Maths Chapter 11 Construction Of Circumcircle And Incircle Of A Triangle Exercise 11.2

WBBSE Solutions For Class 10 Maths Chapter 11 Construction Of Circumcircle And Incircle Of A Triangle Exercise 11.2

Question 1. Let us draw the following triangles and by drawing the incircle of each circle, let us write by measuring the length of the inradius in each case.

1. The lengths of the three sides are 7 cm, 6 cm, and 5.5 cm. 

Solution: The radius of the incircle is 1.8 cm.

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Question 2. The length of the two sides is 7.6 cm and 6 cm and the angle included by those two sides is 75°.

Solution: The radius of the incircle is 2 cm.

Question 3. The length of one side is 6.2 cm and the measures of two angles adjacent to this side are 50° and 75°.

Solution: The radius of the incircle is 1.8 cm.

Question 4. A triangle is a right-angled triangle whose two sides containing the right angle have lengths of 7 cm and 9 cm.

Solution: Radius of the incircle = 2.2 cm.

 

Question 5. A triangle is an isosceles triangle whose two sides containing the right angle have lengths of 7 cm and 9 cm.

Solution: Radius of the incircle = 1.8 cm.

Question 6. The triangle is an isosceles triangle having 7.8 cm. The length of the base and the length of each equal side are 6.5 cm and 10 cm.

Solution:

Given

The triangle is an isosceles triangle having 7.8 cm. The length of the base and the length of each equal side are 6.5 cm and 10 cm.

Length of the inradius = 2.1 cm.

Question 7. A triangle is an isosceles triangle having a 10 cm length of the base and each of the equal angles is 45°.

Solution:

Given

A triangle is an isosceles triangle having a 10 cm length of the base and each of the equal angles is 45°.

Length of the radius of the incircle = 2.1 cm.

Question 8. Let us draw an equilateral triangle having a 7 cm length on each side. By drawing the circumcircle and incircle, let us find the length of the circumradius and inradius and let us write whether there is any relation between them.

Solution: ABC in an equilateral triangle. Here the length of in circle of two triangles is 2 cm & length of the radius of the circumcircle is 4 cm.

∴ Circumcircle = 2 x in radius