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In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP?
- a)3 + √10 : 3 – √10
- b)3 + √8 : 3 – √8
- c)3 + √3 : 3 – √3
- d)3 : √3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a circle of radius 3 units, a diameter AB intersects a chord of len...
In the figure, AB is the diameter of the circle and XY is the chord
Since the diameter intersects the chord perpendicularly, chord will be divided into 2 equal parts of length 1 unit.
⇒ PY = 1 unit and Radius OY = 3 units
⇒ OP2 = 9 – 1
⇒ OP = √8 units
⇒ AP = AO + OP = 3 + √8 and BP = BO – OP = 3 – √8
∴ AP : BP = 3 + √8 : 3 – √8
⇒ OP2 = 9 – 1
⇒ OP = √8 units
⇒ AP = AO + OP = 3 + √8 and BP = BO – OP = 3 – √8
∴ AP : BP = 3 + √8 : 3 – √8
Most Upvoted Answer
In a circle of radius 3 units, a diameter AB intersects a chord of len...
We can start by drawing a diagram of the given information.
First, draw a circle with a radius of 3 units. Then, draw a diameter AB. The midpoint of AB, which we'll call O, is the center of the circle.
Next, draw a chord of length 2 units that intersects AB perpendicularly at point P.
Now, let's analyze what we know about the given information.
The radius of the circle is 3 units.
Since AP is perpendicular to the chord, it must be the radius of the circle. Therefore, AP = 3 units.
Since P is the midpoint of the chord, PB must also be 1 unit.
Now, let's find the length of AB.
Since AP is a radius of the circle, and AB is a diameter, we can use the Pythagorean theorem to find the length of AB.
AB^2 = AP^2 + PB^2
AB^2 = 3^2 + 1^2
AB^2 = 9 + 1
AB^2 = 10
AB = √10 units
So, the length of AB is approximately 3.16 units.
First, draw a circle with a radius of 3 units. Then, draw a diameter AB. The midpoint of AB, which we'll call O, is the center of the circle.
Next, draw a chord of length 2 units that intersects AB perpendicularly at point P.
Now, let's analyze what we know about the given information.
The radius of the circle is 3 units.
Since AP is perpendicular to the chord, it must be the radius of the circle. Therefore, AP = 3 units.
Since P is the midpoint of the chord, PB must also be 1 unit.
Now, let's find the length of AB.
Since AP is a radius of the circle, and AB is a diameter, we can use the Pythagorean theorem to find the length of AB.
AB^2 = AP^2 + PB^2
AB^2 = 3^2 + 1^2
AB^2 = 9 + 1
AB^2 = 10
AB = √10 units
So, the length of AB is approximately 3.16 units.
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In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP?a)3 + √10 : 3 – √10b)3 + √8 : 3 – √8c)3 + √3 : 3 – √3d)3 : √3Correct answer is option 'B'. Can you explain this answer?
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In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP?a)3 + √10 : 3 – √10b)3 + √8 : 3 – √8c)3 + √3 : 3 – √3d)3 : √3Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP?a)3 + √10 : 3 – √10b)3 + √8 : 3 – √8c)3 + √3 : 3 – √3d)3 : √3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP and BP?a)3 + √10 : 3 – √10b)3 + √8 : 3 – √8c)3 + √3 : 3 – √3d)3 : √3Correct answer is option 'B'. Can you explain this answer?.
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