In a circle, if the radius is 5 cm and a chord is 8 cm long, what is the distanc

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Question: In a circle, if the radius is 5 cm and a chord is 8 cm long, what is the distance from the center of the circle to the chord?

Options:

Correct Answer: 4

Solution:

Using the formula d = √(r^2 - (c/2)^2): d = √(5^2 - (8/2)^2) = √(25 - 16) = √9 = 3.

In a circle, if the radius is 5 cm and a chord is 8 cm long, what is the distance from the center of the circle to the chord?

In a circle, if the radius is 5 cm and a chord is 8 cm long, what is the distance from the center of the circle to the chord?

Step 1: Identify the radius of the circle, which is given as 5 cm.
Step 2: Identify the length of the chord, which is given as 8 cm.
Step 3: Calculate half the length of the chord. Since the chord is 8 cm long, half of it is 8/2 = 4 cm.
Step 4: Use the formula d = √(r^2 - (c/2)^2) to find the distance from the center of the circle to the chord.
Step 5: Substitute the values into the formula: d = √(5^2 - (4)^2).
Step 6: Calculate 5^2, which is 25.
Step 7: Calculate (4)^2, which is 16.
Step 8: Subtract 16 from 25: 25 - 16 = 9.
Step 9: Take the square root of 9, which is 3.
Step 10: Conclude that the distance from the center of the circle to the chord is 3 cm.

Circle Geometry – Understanding the relationship between the radius, chord length, and distance from the center to the chord.
Pythagorean Theorem – Applying the theorem to find the distance from the center of the circle to the chord using right triangle properties.