Q12 of 31 Page 218

The lengths of radii of two circles are 8cm and 3 cm and distance between two centre is 13 cm. let us find the length of a common tangent of two circles.

Capture.JPG


A and B are the centre of the two circles


CD is the common tangent


Radius of circle A = 8 cm


Radius of circle B = 3 cm


AB = 13 cm


Since ED∥ AB so


ED = 13 cm


EC = (8-3) = 5cm


Applying Pythagoras theorem in Δ CED we get


Length of tangent = √(132-52)


⇒ Length of tangent = √ 144 = 12 cm


More from this chapter

All 31 →
12

In the adjoining figure O is the centre and BOA is a diameter of the circle. A tangent drawn to a circle at the point P intersects the extended BA at the point T. If ∠PBO = 30°, let us find the value of ∠PTA.

 12

In the adjoining figure, ΔABC circumscribed a circle and touches the points P,Q,R. If AP = 4 cm, BP = 6cm, AC = 12 cm and BC = x cm, let us determine the value of x.

 12

In the adjoining figure, three circles with centre A, B, C touch one another externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, let us find the length of radius of circle with centre A.

 12

In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circle at the points P and Q respectively. A tangent drawn at another point R of a circle intersects CP and CA at the points A and B respectively. If CP = 11 cm. and BC = 7cm, let us determine the length of BR.