SOLUTION: <a href="http://tinypic.com" target="_blank"><img src="http://i42.tinypic.com/m9or3r.jpg" border="0" alt="Image and video hosting by TinyPic"></a> In the diagram PQ and PS are tan

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Question 179524:
In the diagram PQ and PS are tangents drawn to circle O, and chord QS is drawn.
If m< P = 40, what is m< PQS?
Please Help! Thanks!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
It turns out that tangent lines (that are NOT parallel) will intersect somewhere outside the circle and the segments from that intersection to the circle are equal.

So this means that PQ = PS

Since PQ = PS, this shows us that triangle PQS is an isosceles triangle. Consequently, this means that angle PQS = angle PSQ. These are the base angles of the triangle

Because ALL angles of a triangle add to 180 degrees, this means that

angle PQS + angle PSQ + angle QPS = 180

Note: angle P is the same thing as angle QPS

angle PQS + angle PSQ + 40 = 180 ... Plug in angle QPS = 40 (this is given)

angle PSQ + angle PSQ + 40 = 180 ... Plug in angle PQS = angle PSQ

2*angle PSQ + 40 = 180 ... Combine like terms.

2*angle PSQ = 180 - 40... Subtract 40 from both sides.

2*angle PSQ = 140... Combine like terms.

angle PSQ = 140/2... Divide both sides by 2.

angle PSQ = 70... Divide.

So angle PSQ = 70 degrees (this is the lower base angle)

Since angle PQS = angle PSQ, this means that angle PQS = 70 degrees also.

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Answer:

So angle PQS = 70 degrees