Question

The length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm is
A. √7 cm
B. 2√7 cm
C. 10 cm
D. 5 cm

Answer 1

Answer:

Using Pythagoras theorem you can calculate.

Answer: B

Answer 2

The length of the tangent can be calculated using the Pythagorean Theorem as it is a right angled triangle.

Explanation:

PAC is a right angled triangle that is right angled at A.

So, <PAC = 90˚.

Also, we are given that AC (radius) = 6cm.

As P is the point and C the center, so PC = 8cm.

PA = ? cm.

Now by Pythagoras Theorem, we have PA^2 + AC^2 = PC^2.

 Or, PA^2 = PC^2 – AC^2.

  PA^2 = 8^2 – 6^2

  PA^2 = 64 – 36

  PA^2 = 28

  PA = √28     ( we can write 28 as factors 7 X 4)

    PA = 2√7 cm.

So here the correct answer is option B.