Find the length of the tangent to a circle with centre ‘O’ and radius = 6 cm. from a point P such that OP = 10 cm.

Step 1: Recall the tangent properties
NOTE: Tangent is perpendicular to the radius at the point of
contact(tangency)
EXAMPLE: Here PA is tangent segment and OA is radius of circle.
Step 3: Remember the Pythagoras theorem to find the unknown length
NOTE: We can form a right angle triangle by adding the centre and the end
point of the tangent
(Pythagoras theorem) side^2 + side^2 = (hypotenuse)^2
Step 4: Substitute given values in the Pythagoras theorem and simplify the
equation.
EXAMPLE: OP^2 = OA^2 + PA^2 (Pythagoras theorem)
10^2 = 6^2 + PA^2
100 = 36 + PA^2
PA^2 = 100 - 36 = 64
∴ PA = 64 = 8 cm