Question

In triangle ABC, AB = 8cm, BC = 6cm , AC = 10cm. 

1. What kind of triangle is this?

2. What is the position of B based on the circle with AC as the diameter? Why?

3. What is the position of A based on the circle with BC as the diameter? Why?

4. What is the position of the point C based on the circle with diameter AB?

Answer 1

In Δ ABC

AB² + BC² = 8² + 6² = 64 + 36 = 100 = AC² 

Δ ABC is a right angled triangle.

If we draw a circle taken in a AC as diameter, ∠B = 90°, Therefore the point B on the circle.

Δ ABC is a right-angled triangle. 

If we draw a circle taking BC as diameter,

∠A < 90°, Therefore the position of point A will be outside the circle.

If we draw a circle taking AB as diameter, 

∠C < 90°, Therefore the position of point C will be outside the circle.