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AB and CD are 2 parallel chords of a circle which has a radius of 10 units. Parallel chords are 14 units apart such that one of the chords has a length of 12 units. What is the length of non-parallel side of trapezium ABCD
- a)10√2
- b)15√6
- c)6√5
- d)20
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
AB and CD are 2 parallel chords of a circle which has a radius of 10 u...
Since the radius of the circle is 10 and the chords are 14 units apart, both of them have to be on the opposite side of the centre, let CD = 12. It can be shown as
E and F are the midpoint of respective chords.
From the properties of the circle, we know that OF is the perpendicular bisector of DC. Thus DF = 6 and OD =10(radius). It gives OF = 8 (from Pythagoras theorem)
Since it is given that EF = 14, it implies that EO = 14-OF =14-8 = 6
EOB is also a right-triangle such that EO = 6 and OB = 10. This gives EB = 8 or AB = 16.
Since they are symmetrical the trapezium will look like this
From pythogoras we find that AD2 = 142 + 22 = 196 + 4 = 200
AD = 10√2
E and F are the midpoint of respective chords.
From the properties of the circle, we know that OF is the perpendicular bisector of DC. Thus DF = 6 and OD =10(radius). It gives OF = 8 (from Pythagoras theorem)
Since it is given that EF = 14, it implies that EO = 14-OF =14-8 = 6
EOB is also a right-triangle such that EO = 6 and OB = 10. This gives EB = 8 or AB = 16.
Since they are symmetrical the trapezium will look like this
From pythogoras we find that AD2 = 142 + 22 = 196 + 4 = 200
AD = 10√2
Most Upvoted Answer
AB and CD are 2 parallel chords of a circle which has a radius of 10 u...
Let O be the center of the circle. Since AB and CD are parallel chords, then the distance between the chords is equal to the perpendicular distance between the chords and the center O. Let this distance be h.
Since AB and CD are 14 units apart and one of the chords has a length of 12 units, then the other chord must have a length of 12 + 14 = 26 units.
In right triangle OAB, the hypotenuse is the radius of the circle, which is 10 units. The base AB is 12 units, and the perpendicular distance h is the height of the triangle.
Using the Pythagorean theorem, we can find h:
h² = 10² - 12²
h² = 100 - 144
h² = -44
Since h² is negative, there is no real solution for h. This means that the given information does not form a valid trapezium.
Since AB and CD are 14 units apart and one of the chords has a length of 12 units, then the other chord must have a length of 12 + 14 = 26 units.
In right triangle OAB, the hypotenuse is the radius of the circle, which is 10 units. The base AB is 12 units, and the perpendicular distance h is the height of the triangle.
Using the Pythagorean theorem, we can find h:
h² = 10² - 12²
h² = 100 - 144
h² = -44
Since h² is negative, there is no real solution for h. This means that the given information does not form a valid trapezium.
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AB and CD are 2 parallel chords of a circle which has a radius of 10 units. Parallel chords are 14 units apart such that one of the chords has a length of 12 units. What is the length of non-parallel side of trapezium ABCDa)10√2b)15√6c)6√5d)20Correct answer is option 'A'. Can you explain this answer?
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