Perpendicular from the Center to a Chord Bisects the Chord
Two concentri...
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.
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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