Step 1: Draw the diagram according to the given instructions.

NOTE: We are given two concentric circles C_1 \text{and} C_2 with centre O and a chord AB of the larger circle C_1, touching the smaller circle C_2 at the point P.

Step 2: Connect the two points, center and the tangency (touching point of the tangent) and verify that they are perpendicular or not.

NOTE: Tangent and the radius are always perpendicular

Step 3: Join the points, center and the end points of the chord to form right triangles

Step 3: Find the unknown values by the Pythagoras theorem.

NOTE: Recall the Pythagoras theorem

(Hypotenuse)^2 = (height)^2 + (Base)^2

Step 4: Substitute the given values Pythagoras formula and simplify for the unknown values

EXAMPLE: OA^2 = OP^2+ AP^2

5^2 = 3^2 + AP^2

25 - 9 = AP^2

AP= \sqrt{16}

AP = 4 cm