Question

In circle O, diameter AB has been drawn. Locate point C anywhere between A and B (on either side of the diameter). Draw in AC and BC . What type of triangle is ACB ? Explain.

Answer 1

Answer:

Right Triangle.

Step-by-step explanation:

Given AB is a diameter of a circle O.  

Point C is located on the circle's circumference as shown in the attached diagram.

$\angle AOB=180^\circ$

Theorem: The angle at the centre is twice the angle at the circumference.

The angle formed at centre O by arc AB is $\angle AOB$

The angle formed at the circumference at point C by arc AB is $\angle ACB$

By the theorem above:

$\angle AOB=2*\angle ACB\\180^\circ=2*\angle ACB\\\angle ACB=90^\circ$

Therefore, Triangle ACB is a Right Triangle with the right angle at C.