THE PARALLEL CHORD OFA CIRCLE ARE OF LENGTH 6CM,RADIUS OF THE CIRCLE IS 5CM FIND THE DISTANCEBETWEEN THE CHORD
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
Between the chord and what?
Draw a diagram. It is clear that the distance of chord from center:
d^2 + (6/2)^2 = 5^2
the chords are 2d apart.
To find the distance between the parallel chord of a circle, we can use the following steps:
Step 1: Draw a diagram to visualize the problem. Draw a circle with a radius of 5 cm. Mark the chord with a length of 6 cm and label the points of intersection of the chord with the circumference as A and B.
Step 2: Recall the properties of a circle. The perpendicular bisector of a chord passes through the center of the circle. Connect the points A and B to the center of the circle to form radii.
Step 3: Now, you have an isosceles triangle OAB, where O is the center of the circle. The perpendicular bisector of a chord creates two congruent right triangles, OAD and OBD.
Step 4: Since the radius of the circle is 5 cm, each side of the right triangle OAD and OBD is 5 cm.
Step 5: The chord (AB) divides the triangle into two congruent right triangles. Therefore, the hypotenuse of each right triangle is half the length of the chord, which is 6 cm/2 = 3 cm.
Step 6: Use the Pythagorean theorem to find the distance between the chord and the center of the circle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the theorem to triangle OAD, we have:
OA^2 = AD^2 + OD^2
Substituting the known values, we have:
5^2 = AD^2 + OD^2
25 = AD^2 + OD^2
Similarly, in triangle OBD:
25 = BD^2 + OD^2
Step 7: Since both triangles are congruent, AD is equal to BD. Therefore, we can add the two equations together:
25 + 25 = AD^2 + BD^2 + OD^2 + OD^2
50 = 2(AD^2 + OD^2)
Simplifying further:
25 = AD^2 + OD^2
Step 8: Substitute the values from the known lengths:
25 = (3 cm)^2 + OD^2
25 = 9 cm + OD^2
Subtracting 9 cm from both sides:
16 = OD^2
Step 9: Take the square root of both sides:
√16 = √OD^2
4 = OD
Therefore, the distance between the chord and the center of the circle (OD) is 4 cm.