SOLUTION: Question: Find the measeurement of angle APC Known Line AP has a point B on it Line PC has a point D on it Lines AB and CD are the same length Lines AB and CD are both Chords

Question 1956: Question: Find the measeurement of angle APC
Known
Line AP has a point B on it
Line PC has a point D on it
Lines AB and CD are the same length
Lines AB and CD are both Chords of a circle
The measurement of Arc ACD is 200 degrees
Point P is outside the circle
Is there enough information to determine the measeurement of angle APC?
Answer by longjonsilver(155): please explain what "measurement of arc acd = 200 degrees" means since an arc will have a length, not an angle, so which angle do you mean?
Jon
Let me restate the problem as it was originally presented. The notes above are my interpertation of the problem. Hope this helps.

A circle with two secants that have a common end point that is outside of the circle. the end point is named p, the top secant is abp and the bottom secant is named cdp, ab and cd are congruent, the measurment of acd is 200 dedrees, so is cab.
I need to find angle APC

Found 2 solutions by longjonsilver, khwang:
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
cheers for the original...the thing i have issue with is the value 200degree for the angle ACD and CAB. We usually quote internal angles, but the triangle ACP already has 400 degrees worth of angles.
I basically have a triangle ACP and a circle drawn such that A and C are on the circumference and P is outside. Between A and P the line cuts the circle again at B and again, between C and P the line cuts the circle again at D.
AB is equal in length to CD.
Only stumbling block is the value 200.
Jon

Answer by khwang(438) (Show Source):
You can put this solution on YOUR website!
You are right arc ACD having the 1 dim length not an angle,but the
permeter of the whole circle is 360 deg, so an arc of 200 deg means an arc
of length 2 pi r * 200/360. Let O be the center of the circle.
Degree of Arc ACD = degree of the angle AOD(facing the arc ACD).
P

B D
A C
Now, arc ACD = 200 deg =arc BAC
arc ABD = 160 deg ((= 360 -200) = arc BDC
angle ACD = half of arc ABD = 160 * 1/2 = 80 deg
Similarly, angle BAC = 80 deg
Hence, in the triangle APC, we see that
angle APC = 180 - 80*2 = 20 deg
Kenny