Geometry Problem Help Please? WILL pick top answer

Two segments from P are tangent to O. If angle P
60 and the
radius of
O is 12 feet, find the length of each tangent
Segment


Each side of a circumscribed equilateral triangle is 16 meters.
Find the radius of the circle.

It is hard to read your question, because the symbol between P and 60 does not display on Firefox or
Safari in Windows XP. Internet Explorer 8 is worse. Same is true for symbol between of and in radius
of O

I will assume it says if angle P has a measure of 60° and the radius of circle O is 12 feet, we can
label the points of tangency as A and B and the center of the circle as C
so CA= 12 and CB=12 since they are radii.





There is a theorem that

If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.

Thus CA is perpendicular to AP and CB is perpendicular to BP


Moreover AP is congruent to BP so APB is an isosoles triangle with a vertex angle of 60
and two congruent angles at A and B. Since these two angles are congruent, they sum to
120° = 180° - 60° so angles PAC and PBC are congruent, summing to 120° thus they are
60° too so triangle PAB is equilateral.

Moreover, the angles of the inscribed triangle ACB are each 30° summing to 60 so the inscribed
triangle has an obtuse angle of 120°

If we plot point M as a midpoint to segment AB and drop a perpendicular to segment AB from C to
M, it will form two 30° 60° 90° triangles sharing a common perpendicular of length 6 and the
segment AM will be 6√3

The segment AB will be twice that or 12√3 and since the APC triangle is equilateral, each
of tangents AP and BP will have length

12√3 feet
I don't like to write numerical approximations, these
can be calculated with a computer or calculator
but it is approximately 20.78 feet

The other answerer did good work but made a slight error on calculating the