Question no.5:

5. In the adjoining figure, the diameter CD of a circle with centre O is perpendicular to the chord AB. If AB=8 cm and CM=2 cm, find the radius of the circle. 


Dear student,
Here is the solution of your asked query:
Let the radius of the circle be r.OA=OC=rWe know that the perpendicular from center to the chord of the circle bisects the chord.So, AM=BMAM=12AB=12×8=4cmAlso, OC=OM+CM=rOM+2=rOM=r-2            Now considering right triangle AMO, we have;OA2=OM2+AM2       {using Pythagoreous theorem}r2=r-22+42r2=r2+4-4r+164r-4=164r=20r=5Therefore, radius of circle is 5 cm.
Regards

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