Question

Point P is 10 cm from the centre of a circle of radius 4 cm. Tangents are drawn from P to the circle. Find the angle between the tangents.

Answer 1

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)

Answer 2

Answer:

one-fourth of a number is 9