Trigonometry / Pythagoras' Theorem Help

[Student 26607]

Hi, I got some homework and I don't understand them or know what to do. I think that they're either Trigonometry or Pythagoras' Theorem based, it would be much appreciated if someone could help me please.

Here are the questions:

Two tangents are drawn from P to meet a circle at points D and F. If the circle has a circumference of 18.5 metres and the angle between the tangents is 38º, find:
a) The length of PF
b) The distance from P to the centre of the circle.

It would really help if you could also show how you got it (it would help my understand as well as pass ).

Thanks for reading this, I hope someone will be able to help me with my dillema.

- Student 26607

 

[wjm11]

Two tangents are drawn from P to meet a circle at points D and F. If the circle has a circumference of 18.5 metres and the angle between the tangents is 38º, find:
a) The length of PF
b) The distance from P to the centre of the circle.

Draw yourself a picture: a circle with the two tangent lines. From the tangent points, draw radii to the center of the circle, O. Draw a line from the center of the circle, O, to point P. Facts: the tangent lines and the radii are perpendicular to each other, i.e., angle OFP is 90 degrees; the angle between the tangents is given as 38 degrees; line OP will bisect this angle; the circumference is 18.5; you can calculate the radius. You now have enough information about triangle OFP to solve for all angles and sides using basic trigonometry.