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Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.?
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Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are...
Suppose, we say that the radius of the circle is r cm, and the distance from the center to the larger chord perpendicular to it is OB=h cm; therefore, distance to the smaller chord perpendicular to it will be OC=h+7 cm, because the distance between the chords are 7 cm, which adds up with h. And we can say that AB and CD are half of the chords, so AB=12 cm and CD=5 cm respectively. Pardon me because I have used terms AB and CD as the half of the chords, where they were supposed to mean the full length of the chords, which was a mistake from my part.
Now, according to pythagoras theorem, we can determine two equations from the picture, such as:
From OAB, r2=h2+122
From OCD, r2=(h+7)2+52
We can equate the equations as both sides of them contains r2, so,
h2+122=(h+7)2+52
Solving this equation, we easily get, h=5 cm. Plugging this value in the very 1st equation, we can find r=13 cm. So, the diameter will be, d=r∗2=26 cm.
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Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.?
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Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.?.
Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two chords ab, cd of lengths 24 cm, 10 cm respectively of a circle are parallel. the chords lie on the same side of the centre and the distance between them is 7 cm, then find the length of the diameter of the circle.?.
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