Question

the vertices of AABC lie on a circle and AB is a diameter of thar circle, then ZACB is a right angle Proof: Since AB is a diameter of the circle, the midpoint of AB must be the center of the circle. Denote the center by O. Then 0 = 0B a OC by (Justification 1). By the (Justification 2) we have LOAC = LOCA and LOBCA LOCB. Let = N(COAC) and 8 - (LOBC). Then 2a + 28 180" by the Justification 3). Thus a + B = 90º and ZACB is a right angle. 1. by construction 2. That's what we want to show 3. given Justification 3 4. Euclidean Angle Sum Theorem Justification 1 5. Isosceles Triangle Theorem Justification 2 6. by ASA 7. by CPCTC 8. definition of the triangle 9. definition of the circle

Answer 1