Two circles with centre o and radius r and with centre o' and radius r/2 touch each other internally at a point A and AB is a chord of the bigger circle intersecting smaller circle at P . If o , o' and A lie on a straight line , prove that AP = AB .
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clearly o , o' and A lie on a straight line
B , P and A lie on a straight line
in smaller circle,o'A is diameter
angle o'PA=90 ,o'P is perp on AB
for bigger circle,lets drop perp OL on AB
tr Ao'P similar tr AOL
therefore,OL is perp on AB & L bisects AB
AP=1/4 AB
B , P and A lie on a straight line
in smaller circle,o'A is diameter
angle o'PA=90 ,o'P is perp on AB
for bigger circle,lets drop perp OL on AB
tr Ao'P similar tr AOL
therefore,OL is perp on AB & L bisects AB
AP=1/4 AB
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