Calculate the radius of a circle in which a chord of length 10 cm is 12 cm from the centre
draw the radius which bisects the chord, and another to the end of the chord. Now you have a right triangle with legs 5 and 12. So, the hypotenuse (the radius of the circle) is 13.
To calculate the radius of a circle in which a chord of length 10 cm is 12 cm from the center, you can use the following steps:
Step 1: Draw a diagram: Start by drawing a circle and marking its center. Label the center as point O. Draw a chord AB with a length of 10 cm, and mark point C on the chord such that OC is 12 cm.
Step 2: Identify the Perpendicular Bisector: Draw a perpendicular bisector to the chord AB passing through point O. Let the intersection point between the perpendicular bisector and chord AB be point D.
Step 3: Apply the Pythagorean Theorem: The distance from the center of the circle to the midpoint of the chord is the radius of the circle. In this case, length OD is the radius. Using the Pythagorean theorem, we can calculate OD.
Since OC is 12 cm and DC is half the length of the chord AB (which is 10 cm/2 = 5 cm), we can apply the Pythagorean theorem as follows:
OD^2 = OC^2 - DC^2
OD^2 = 12^2 - 5^2
OD^2 = 144 - 25
OD^2 = 119
Step 4: Calculate the radius: Take the square root of both sides to find OD, which is the radius of the circle:
OD = √119
So, the radius of the circle is approximately equal to √119 cm.