Two concentric circles of radii 5cm and 3cm
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two concentric circles are of radii 5cm and 3cm. length of the chord of the larger circle, (in cm), which touches the smaller circle is.?
Answered by admin @
Let the radius of the bigger circle be 'R' and the radius of the smaller circle be 'r'.
It is given that R=5cm=OB and r=3cm=OD and AB is the chord whose length we have to find.
AD=BD and OD⊥AB(radius is perpendicular to a chord and it divides the chord into two equal parts)
therefore, ΔODB is a right angled triangle
where, OD²+BD²=OB²
(3)²+BD²=(5)²
9+BD²=25
BD²=25-9
BD²=16
BD=4cm
Since AD=BD=4cm
therefore, AB=AD+BD
AB=4+4
AB=8cm
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