Q4 of 35 Page 11

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

Let the centre of circle be O so that PO = 13 cm


Tangent is PB whose length is 12 cm


OB is radius as shown



Now we know that radius is perpendicular to point of contact


Hence OB is perpendicular to PB


Hence ∠PBO = 90°


Consider ΔPBO


Using Pythagoras theorem


⇒ PB2 + OB2 = PO2


⇒ 122 + OB2 = 132


⇒ OB2 = 132 - 122


⇒ OB2 = 169 – 144


⇒ OB2 = 25


⇒ OB = ±5


As length cannot be negative


⇒ OB = 5 cm


Hence length of radius is 5 cm


More from this chapter

All 35 →
2

Rajesh is 29 m away from the centre of a circular flower bed. Find the distance he has to cover to reach the flower bed along the tangential path if the radius of the flower bed is 20m.

 3

Find the length of the tangent drawn from a point, whose distance from the centre of a circle is 5c, and the radius of the circle is 3 cm.

 5

If d1, d2 (d2<d1) are the diameters of two concentric circles and chord of one circle of length C is tangent to other circle, then prove that d22 = C2 + d12.

 6

Prove that the line segment joining the point of contact of two parallel tangents to a circle is a diameter of the circle.