Question

the radii of 2 concentric circles are 13cm and 8cm. AB is a diameter of bigger circle and BD is tangent to smaller circle touching it at D and intersecting the larger circle at P, on producing. Find length AP

Answer 1

in odb, ob=13cm, od =8cm
bd=√(13^2-8^2)
=√105
pb=√105 +√105
ab=13+13=26
ap=√(ab^2-pb^2)
=√(26^2-2×√105^2)
=√676-420
= √256
=16cm

Answer 2

OB=13 CM, OD= 8 CM, OP= 8 CM AND AB=26 CM
ANGLE APD =90 DEGREE AND ANGLE ODB = 90 DEGREE
HENCE TRIANGLE APB AND ODB ARE SIMILAR
THEREFORE
AP/OD=AB/OB
HENCE AP= (OD*AB)/OB
= (8*26)/13
= 16
AP =16 CM