Question

find the length of a tangent drawn from a point 10cm away from the centre of a circle of radius 6cm

Answer 1

let O be the Centre of the circle
and AB be the tangent and OA be the radius

therefore AB is perpendicular to OA(tangent is perpendicular to the radius)
therefore triangle AOB is a right angled triangle.with OB as it's hypotenuse.

therefore by Pythagoras theorem
in triangle AOB
AB^2+(6)^2=(10)^2
=>AB=√100-36
=>AB=8cm

therefore the length of the tangent is 8cm.


I hope this will help you.

Answer 2

Thank you for asking this question:

Here is your answer.

The question has some options too, below are the missing options:

a) √7 cm

b) 2√34 cm

c) 16 cm

d)8 cm

The correct answer is Option D: 8cm

In ΔOPQ, ∠Q = 90°

∴ OP² = OQ² + PQ²

10² = 6² + PQ²

PQ² = 100 - 36

= 64

PQ = 8 cm

If there is any confusion please leave a comment below.