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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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