A chord 20cm long is 12cm from the center of a circle calculate, correct to one decimal place
draw a diagram. Cut the chord in half with a radius drawn through its center.
Now you can see that the radius r is
r^2 = 10^2 + 12^2
If the radius is not what you want, then maybe you should have proofread your post...
radius =15.6205
angle substended=79.62
be the angle between the radius and length of the
chord from the centre. Then,
. Therefore, angle subtended by the chord at the centre
of the circle is 2
39.8o = 79.60 (Correct to 1 decimal place).
Also, in part (b) (ii), the perimeter of the minor segment
is
, where
= 15.62 cm.
To calculate the radius of the circle, we can use the properties of a circle and the given information about the chord and its distance from the center.
First, we need to recall a theorem about the relationship between a chord and its distance from the center of a circle. The perpendicular bisector of a chord passes through the center of the circle. This means that the line connecting the center of the circle to the midpoint of the chord is perpendicular to the chord itself.
In our case, we have a chord that is 20 cm long and is located 12 cm from the center of the circle. Since the line connecting the center of the circle to the midpoint of the chord is the perpendicular bisector, we can draw a line from the center to the midpoint of the chord, which will bisect the chord into two equal segments.
Thus, we can divide the chord into two segments: half of the chord length on one side (10 cm) and the distance from the center to the midpoint of the chord on the other side (12 cm).
Now, we have a right triangle with sides measuring 10 cm and 12 cm and we need to find the length of the hypotenuse, which is equal to the radius of the circle.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse^2 = base^2 + height^2
radius^2 = 10^2 + 12^2
radius^2 = 100 + 144
radius^2 = 244
To find the radius, we can take the square root of both sides:
radius = √(244)
radius ≈ 15.6 cm (rounded to one decimal place)
Therefore, the correct answer to the question is that the radius of the circle is approximately 15.6 cm.