1. ## triangle geometry

The attached jpeg shows a triangle within a circle. The problem is to find the angle BCD. Anyone know how to do this?

2. Originally Posted by marcvonne
The attached jpeg shows a triangle within a circle. The problem is to find the angle BCD. Anyone know how to do this?
Is $\displaystyle \overline{AC}$ a diameter? If so, $\displaystyle \angle B=90^{\circ}$, and it's easy from there.

3. Yes line AC is a diameter. What is the rule here? Is it because the hypotenuse cuts through the centre?

4. Originally Posted by marcvonne
Yes line AC is a diameter. What is the rule here? Is it because the hypotenuse cuts through the centre?
The rule here is 'if an inscribed angle intercepts a semicircle, then it is a right angle'. An inscribed angle measures one-half its intercepted arc. Angle B intercepts a semicircle and equals one-half the measure of 180 degrees or 90 degrees.

Your angle BCD is an exterior angle to your triangle and is equal to the sum of the two remote interior angles; namely angle B and angle A.

Therefore, angle BCD = 90 + 33 = 123 degrees.

5. Splendid! Thankyou very much for the answer. Now I need to discuss this with my son.