A tangent from point P to a circle of radius 4 cm is 10 cm long.
a) Find the distance of P from the centre of the circle.
b) Find the size of the angle between the tangent and the line joining P to the centre of the circle.
+23254 Draw the circle, include the center, and draw the tangent.
Call the center C, the point of tangency of the circle and the tangent T, and call the point on the tangent P.
The points C, T, and P create a right triangle with a right angle at T.
TC = 4 and PT = 10. Use the Pythagorean Theorem to find the length PC:
PC² = PT² + TC² ---> PC² = 10² + 4² ---> PC² = 116 ---> PC = √116
To find the size of ∠TPC: If you use tangent: tan(∠TPC) = 4/10 ---> ∠TPC = 21.8° (approx)
+23254 Draw the circle, include the center, and draw the tangent.
Call the center C, the point of tangency of the circle and the tangent T, and call the point on the tangent P.
The points C, T, and P create a right triangle with a right angle at T.
TC = 4 and PT = 10. Use the Pythagorean Theorem to find the length PC:
PC² = PT² + TC² ---> PC² = 10² + 4² ---> PC² = 116 ---> PC = √116
To find the size of ∠TPC: If you use tangent: tan(∠TPC) = 4/10 ---> ∠TPC = 21.8° (approx)
