Q. 183.8( 8 Votes )

The radii of two

Answer :

The figure for the above given condition is as shown below,



Now we will join OD, we get



So as per the given criteria,


AB = 26cm, BO = AO = 13cm, OD = 8cm……….(i)


Now consider smaller circle,


In this BD is tangent to the smaller circle given and OD is the radius of the smaller circle,


And we know in a circle tangent is perpendicular to the radius, i.e.,


ODBD


BDO = 90°….(ii)


Now consider bigger circle,


In this P is a point in the semicircle with radius AB,


And we know in a circle, angle in a semicircle is always a right angle, i.e.,


APB = 90°….(iii)


Now we will consider ΔABP and ΔOBD,


APB = BDO = 90° (from equation(ii) and (iii))


ABP = DBO (common angle)


Hence by AA similarity,


ΔABP~ΔOBD


And we know sides of similar triangles are proportional, hence in these two triangles,



Now substituting values from equation (i), we get



AP = 2 × 8


AP = 16cm


Hence the length of AP is 16cm.


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