Question

In the figures two circles with centres A and B touch each other externally .PM=15cm is tangent to a circle with centre A and QN=13cm is tangent to a curcke with centre B frok external points P and Q respectively. If PA =17cm and BQ=12cm ,Find distance between A and B.​

Answer 1

Answer:

The angle between a tangent and radius is right angle.angles BNQ and AMP are right angles

The triangle PAM is a right angled triangle, with PA being the hypotenuse.

Using Pythagoras theorem, the radius of the circle with centre A is found as

AM = Sqrt ( 172 - 152)

AM = 8 cm

Similarly, the radius of circle with centre B is found as

BM= sqrt( 132 -122)

BM = 5cm

Clearly , the distance between the centre is the sum of radii of the two circles ( AC +BC)

Required distance = 5cm + 8cm = 13 cm.