Given: ∆ABC, m∠A = 35° Circle k(O, r=3) O∈ AB Find: Perimeter of ∆ABC

Question

     

Answer 1

When a circle has an inscribed angle (vertex on the circle) that "cuts out" a semi-circle, like the one in the figure you have provided, then the inscribed angle is a right angle. Knowing that ∠C is a right angle, allows you to use the right-triangle trig that Mark has shown you above.

Since you want the perimeter, you will need AC + CB + AB. And since we know that AB is a diameter, its length will be twice the radius you were given. And AC and CB can be found with the trig ratios Mark showed you.

Answer 2

sin 35° = BC / 6

sin 55° = AC / 6

Can you solve for AC and BC and answer?