If a chord of length 10cm is at a distance of 12 cm from the centre of a circle. Find the radius of the circle.
To find the radius of the circle, we can use the relationship between the radius and the distance of a chord from the center of the circle.
Here's how we can solve it step by step:
Step 1: Identify the given values:
- Length of the chord (c) = 10 cm
- Distance from the center of the circle to the chord (d) = 12 cm
Step 2: Draw a diagram:
- Draw a circle with its center.
- Mark the chord inside the circle and label it with its length.
- Mark the distance from the center to the chord.
Step 3: Apply the formula:
- According to the relationship between the radius (r), chord length (c), and distance from the center of the circle to the chord (d):
r^2 = (d^2) + (c/2)^2
Notice that the length of the chord forms a right-angled triangle, with d as one side and half the length of the chord (c/2) as the other side. The radius (r) is the hypotenuse of this triangle.
Step 4: Substitute the values into the formula:
r^2 = (12^2) + (10/2)^2
r^2 = 144 + 25
r^2 = 169
Step 5: Solve for the radius (r):
- To isolate r, take the square root of both sides of the equation:
r = √169
r = 13 cm
Therefore, the radius of the circle is 13 cm.
draw altitude from center of circle to center of chord. length 12
half of chord length 5
5, 12, 13 right triangle results
r = 13