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The perpendicular from the center O of the circle bisects the chord EF. If EF = 30 cm and the radius of the circle is 17 cm, then find the length of the perpendicular OG.
- a)12
- b)8
- c)6
- d)13
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The perpendicular from the center O of the circle bisects the chord E...
Given
EF = 30 cm
Radius = 17 cm
Concept:
Pythagorean theorem
h2 = p2 + b2
Where h, p & b be the hypotenuse, perpendicular & base of triangle
Calculation:
Triangle OEG is a right-angle triangle.
EG = FG = OG/2
The distance of chord from center
∴ The length of the perpendicular OG is 8 cm.
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Community Answer
The perpendicular from the center O of the circle bisects the chord E...
To find the length of the perpendicular OG, we can use the properties of perpendiculars and chords in a circle.
Given:
EF = 30 cm (chord)
Radius of the circle (OB or OA) = 17 cm
First, let's draw a diagram to visualize the problem:
```
A
/ \
/ \
/ \
O ------- B
\ /
\ /
\ /
\ /
C
|
E
|
F
```
We are given that the perpendicular from the center O bisects the chord EF. Let's denote the midpoint of EF as point G. So, OG is the perpendicular from the center O to the chord EF, and it bisects EF at G.
Now, let's use the properties of perpendiculars and chords in a circle.
1. The perpendicular from the center of a circle to a chord bisects the chord.
=> EG = FG = 1/2 * EF = 1/2 * 30 = 15 cm
2. In a circle, a perpendicular drawn from the center of the circle to a chord bisects the chord and is also the radius of the circle.
=> OG = OB = OA = radius of the circle = 17 cm
So, the length of the perpendicular OG is 17 cm.
Therefore, the correct answer is option B) 8 cm.
Given:
EF = 30 cm (chord)
Radius of the circle (OB or OA) = 17 cm
First, let's draw a diagram to visualize the problem:
```
A
/ \
/ \
/ \
O ------- B
\ /
\ /
\ /
\ /
C
|
E
|
F
```
We are given that the perpendicular from the center O bisects the chord EF. Let's denote the midpoint of EF as point G. So, OG is the perpendicular from the center O to the chord EF, and it bisects EF at G.
Now, let's use the properties of perpendiculars and chords in a circle.
1. The perpendicular from the center of a circle to a chord bisects the chord.
=> EG = FG = 1/2 * EF = 1/2 * 30 = 15 cm
2. In a circle, a perpendicular drawn from the center of the circle to a chord bisects the chord and is also the radius of the circle.
=> OG = OB = OA = radius of the circle = 17 cm
So, the length of the perpendicular OG is 17 cm.
Therefore, the correct answer is option B) 8 cm.
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