+279 
Use the diagram. 
is a diameter, and 
.
The figure is not drawn to scale. So Which Statement is NOT True?
A.  | |
B.  | |
C.  | |
D.  |
+129852 A isn't true....
To see why, note that triangle ACP is similar to triangle CBP. Therefore angle CAP = angle BCP. And angle BCP = angle BCD and BCD subtends arc DB. And angle CAP = angle CAB, and angle CAB subtends arc BC. But since CAP = BCP and BCD = CAB, then arc DB = arc BC. But arc BC is much greater than arc AC, therefore, arc BD is much greater than AC.
Just to add another proof to the mix....in any triangle, an angle opposite a greater side is larger than an angle opposite a lesser side. So, in triangle ACB, BC > AC. Therefore, angle CAB > CBA. Then, since they are bpth inscribed angles, the arc intercepted by CAB > the arc intercepted by CBA. And, as was shown above, the arc intercepted by CAB = the arc intercepted by BCD = BD. And the arc intercepted by CBA = AC. Thus, arc BD > arc AC.
+129852 A isn't true....
To see why, note that triangle ACP is similar to triangle CBP. Therefore angle CAP = angle BCP. And angle BCP = angle BCD and BCD subtends arc DB. And angle CAP = angle CAB, and angle CAB subtends arc BC. But since CAP = BCP and BCD = CAB, then arc DB = arc BC. But arc BC is much greater than arc AC, therefore, arc BD is much greater than AC.
Just to add another proof to the mix....in any triangle, an angle opposite a greater side is larger than an angle opposite a lesser side. So, in triangle ACB, BC > AC. Therefore, angle CAB > CBA. Then, since they are bpth inscribed angles, the arc intercepted by CAB > the arc intercepted by CBA. And, as was shown above, the arc intercepted by CAB = the arc intercepted by BCD = BD. And the arc intercepted by CBA = AC. Thus, arc BD > arc AC.
