Question

If the radius of a circle is 2.5 cm the length of the tangent from a point p which is at a distance of 6.5 cm from the centre is

Answer 1

Question :

• If the radius of a circle is 2.5 cm the length of the tangent from a point p which is at a distance of 6.5 cm from the centre is?

Solution :

• Radius = 2.5 cm
• DISTANCE of tangent = 6 cm

Let BP = x cm

We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

In right angled ∆OAP, OA ⟂ AP,

OP² = OA² + AP²

[By Pythagoras theorem]

(2.5 +x)² = (2.5)² + 6²    [OP = OA + BP]

6.25 + x² + 5x = 6.25 + 36

x² + 5x - 36 = 0

x² +9x - 4x -36 = 0

[By factorization]

x(x +9) -4(x +9)=0

(x +9) (x -4) = 0

(x +9) = 0  or (x -4) = 0

x = -9 , x = 4

Sides Can't be negative , so x= 4

Hence, the distance of P from the nearest point of the circle B is 4 cm.