Questions about area circle help please?

Question

In a circle center O, AC perpendicular to OB If OA =2 AC=1 
A) what is the area if triangle ACB 
B)what is the perimeter of triangle OAC?

Answer 1

In a circle center O, AC is perpendecular to OB.

OA = 2 and AC = 1.

• A).

From the given data Triangle AOC is a right triangle.

From the pythagoras theorem : OA² = OC² + AC².

Substitute OA = 2 and AC = 1.

2² = OC² + 1²

OC² = 4 - 1

OC² = 3

OC = √3.

From the diagram, OA and OB are the radius of the circle with center ' O '.

So, OA = OB

OB = OC + CB = 2

√3 + CB = 2

⇒ CB = 2 - √3.

The area of triangle ACB = (1/2) * CB * AC.

Substitute CB = 2 - √3 and AC = 1.

= (1/2) * (2 - √3) * 1

= (2 - √3)/2.

The area of triangle ACB = (2 - √3)/2 square units.

• B).

Perimeter of triangle OAC = OA + AC + OC

= 2 + 1 + √3

= 3 + √3.

Perimeter of triangle OAC = 3 + √3 units.