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# In the diagram shown below, AC is tangent to circle O at A and to circle P at C , OP intersects AC at B , OA = 4, AB = 5, and PC = 10.

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In the diagram shown below, AC is tangent to circle O at A and to circle P at C, OP intersects AC at B, OA = 4, AB = 5, and PC = 10. The measure of angle AOB = ? degrees

The measure of angle PCB = ? degrees

The measure of line segment BC =

May 18, 2020

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Since triangle(OAB) is a right triangle (tangents are perpendicular to radii drawn to the point of contact), tan(AOB)  =  5/4   -->   angle(AOB)  =  tan-1(5/4)  =  ...

Since AC is a tangent and PC is a radius drawn to the point of tangency, angle(PCB)  =  ...

Triangle(OAB) is similar to triangle(PCB), so OA / PC  = AB / BC.

May 18, 2020
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I still don't quite understand how to find the measure of angle AOB or PCB...

GAMEMASTERX40  May 18, 2020
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To  find AOB, as geno points  out, we  need to  take the arctan  (tangent inverse)  to  find  this angle we have

arctan ( 5/4)  ≈  51.3°

Since AC  is  tangent  to circle P   at C  and  PC  is a radius.....there form a right angle

So  angle PCB  =  90°   May 18, 2020