Q. 294.1( 8 Votes )
The radii of two
Given: The radii of two concentric circles with the same center as O are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is tangent to the smaller circle touching it at D and intersecting the larger circle at P, on producing
To Find: length of AP
Construction: Join OD
Clearly OB ⏊ AC [As a tangent to at any point on the circle is perpendicular to the radius through the point of contact]
PD = BD [Perpendicular through the center to a chord in a circle bisects the chord]
i.e. D is the mid-point of BP.
Also, O is the mid-point of AB.
So, We can use the mid-point theorem and we will have
[Mid-point theorem: The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.]
AP = 2OD
OD is radius of smaller circle, therefore
AP = 2(8) = 16 cm
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