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Question
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle (in cm) which touches the smaller circle.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle (in cm) which touches the smaller circle.
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Solution
Let the radius of the bigger circle be 'R' and the radius of the smaller circle be 'r'.
It is given that R=5cm=OA and r=3cm=OP and AB is the chord whose length we have to find.
AP=BP and OP⊥AB(radius is perpendicular to a chord and it divides the chord into two equal parts)
therefore, ΔOPA is a right angled triangle
where, O²+Ap²=OA²
(3)²+AP²=(5)²
9+AP²=25
AP²=25-9
AP²=16
AP=4cm
Since AP=BP=4cm
therefore, AB=AP+BP
AB=4+4
AB=8cm
Let the radius of the bigger circle be 'R' and the radius of the smaller circle be 'r'.
It is given that R=5cm=OA and r=3cm=OP and AB is the chord whose length we have to find.
AP=BP and OP⊥AB(radius is perpendicular to a chord and it divides the chord into two equal parts)
therefore, ΔOPA is a right angled triangle
where, O²+Ap²=OA²
(3)²+AP²=(5)²
9+AP²=25
AP²=25-9
AP²=16
AP=4cm
Since AP=BP=4cm
therefore, AB=AP+BP
AB=4+4
AB=8cm
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