Radius of a circle,13cm. Length of the chords is 10cm find the distance of the chord from the center of a circle
draw two radii
... one to the end of the chord
... the other bisecting the chord
the bisector is perpendicular to the chord
this forms a right triangle
use Pythagoras to find the distance
To find the distance of the chord from the center of the circle, we can use the Pythagorean theorem.
Step 1: Draw a diagram of the circle with the chord and the center of the circle.
Step 2: Connect the center of the circle to the midpoint of the chord, forming a right triangle.
Step 3: Label the radius of the circle as 13 cm.
Step 4: Since the chord is 10 cm long, its midpoint is 5 cm away from each end of the chord.
Step 5: Now we have a right triangle with one leg measuring 5 cm (half the length of the chord) and the hypotenuse measuring 13 cm. We need to find the other leg, which represents the distance of the chord from the center of the circle.
Step 6: Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the formula, we have:
(Other leg)^2 + 5^2 = 13^2
(Other leg)^2 + 25 = 169
Subtract 25 from both sides:
(Other leg)^2 = 144
Take the square root of both sides:
Other leg = √144
Other leg = 12
Hence, the distance of the chord from the center of the circle is 12 cm.