Question
Download Solution PDFThe radii of two concentric circles are 34 cm and 50 cm. A and D are the points on larger circle and B and C are points on smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The radii of two concentric circles are 34 cm and 50 cm.
ABCD is a straight line and BC = 32 cm.
A and D are the points on larger circle and B and C are points on smaller circle.
Concept Used:
Pythagoras theorem
Hypotenuse2 = Perpendicular2 + Base2
Perpendicular drawn from the centre to the chord divide the chord into two equal parts.
Calculation:
BC = 32 cm
BP = 32/2 = 16 cm
In triangle OBP
Apply Pythagoras Theorem
OB2 = BP2 + OP2
342 = OP2 + 162
OP2 = 1156 - 256
OP2 = 900
OP = 30 cm
In triangle OPD
OD2 = OP2 + PD2
502 = 302 + PD2
PD2 = 2500 - 900
PD2 = 1600
PD = 40 cm
AD = 2 × PD = 2 × 40 = 80 cm
The length of AD is 80 cm.
∴ Option 2 is the correct answer.
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