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CBSE - X - Mathematics - Circles

.The Fig., shows two concentric circles with centre O. AB and APQ are tangents to the inner circle from point A lying on the outer circle. If AB=7.5 cm then find AQ

Asked by 28th February 2013, 4:05 PM
Answered by Expert


Join OP. Now since, APQ is a tangent to the smaller circle so, OP = 90 degree. 
Since, the length of tangents drawn from a common point to a circle is equal
So, AB = AP
Also, in the bigger circle, AQ is the chord and OP is the perpendicular to the chord. 

Since, in a circle, a perpendicular drawn from the center of the circle to a chord bisects it. 
Therefore, AP = PQ. 
Hence, AQ = AP+PQ = 2*AP = 2* AB = 2*(7.5) = 15 cm
Answered by Expert 28th February 2013, 4:32 PM

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