In adjoining figure, a chord PQ of a centre O and radius=15 cm is bisected at M by diameter AB. If OM=9cm,find the lengths of (i) PQ (ii) AP (iii) BP

Question

Sir, 

Please respond to my question fast.It would be honour to know rhe answer.

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Answer 1

To find PQ, note that triangle OMQ is a right triangle.  Leg OM=9 and Hypotenuse OQ = 15, so 15²-9²=MQ².  Solving you get MQ = 12.  PQ = 2MQ = 24 cm.

 

Find AP the same way, using the Pythagorean Theorem.  Leg MP = 12 cm, leg MA = 15-9 = 6 cm.  12²+6²=AP².  Solve for AP.

 

Find BP the same way.  Leg MB = 9+15 = 24 cm, leg MP = 12 cm.  24²+12² = BP^2.  Solve for BP.