A circle is inscribed in a triangle. What is the radius of the incircle if the t

₹0.0

📥 Instant PDF Download
♾ Lifetime Access
🛡 Secure & Original Content

What’s inside this PDF?

Question: A circle is inscribed in a triangle. What is the radius of the incircle if the triangle has sides of lengths 7, 8, and 9 units?

Options:

4 square units
3 square units
5 square units
2 square units

Correct Answer: 3 square units

Solution:

The area of the triangle can be calculated using Heron\'s formula. The semi-perimeter s = (7+8+9)/2 = 12. The area A = √(s(s-a)(s-b)(s-c)) = √(12(12-7)(12-8)(12-9)) = √(12*5*4*3) = 12√5. The radius r = A/s = 12√5/12 = √5. The radius is approximately 3 square units.

A circle is inscribed in a triangle. What is the radius of the incircle if the t

Practice Questions

A circle is inscribed in a triangle. What is the radius of the incircle if the triangle has sides of lengths 7, 8, and 9 units?

4 square units
3 square units
5 square units
2 square units

Questions & Step-by-Step Solutions

A circle is inscribed in a triangle. What is the radius of the incircle if the triangle has sides of lengths 7, 8, and 9 units?

Step 1: Identify the lengths of the sides of the triangle. They are 7, 8, and 9 units.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2. Here, s = (7 + 8 + 9) / 2 = 12.
Step 3: Use Heron's formula to find the area (A) of the triangle. The formula is A = √(s(s-a)(s-b)(s-c).
Step 4: Substitute the values into Heron's formula. A = √(12(12-7)(12-8)(12-9)).
Step 5: Calculate the differences: (12-7) = 5, (12-8) = 4, (12-9) = 3.
Step 6: Now substitute these values back into the formula: A = √(12 * 5 * 4 * 3).
Step 7: Calculate the product inside the square root: 12 * 5 = 60, then 60 * 4 = 240, and finally 240 * 3 = 720.
Step 8: Now find the square root: A = √720. This can be simplified to A = 12√5.
Step 9: To find the radius (r) of the incircle, use the formula r = A / s.
Step 10: Substitute the area and semi-perimeter into the formula: r = (12√5) / 12.
Step 11: Simplify the expression: r = √5.
Step 12: The radius of the incircle is approximately 3 square units.

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Incircle Radius – The radius of the circle inscribed within a triangle, calculated using the area and semi-perimeter.
Semi-perimeter – Half of the perimeter of the triangle, used in the calculation of the area and incircle radius.

A circle is inscribed in a triangle. What is the radius of the incircle if the t

What’s inside this PDF?

A circle is inscribed in a triangle. What is the radius of the incircle if the t

Practice Questions

Questions & Step-by-Step Solutions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?