Two chords of a circle of lengths 10 cm and 8 cm are at the
distances 8.0 cm and 3.5 cm, respectively from the centre?
ans:false how? plzz explain clearly
To determine whether the statement is true or false, we can use the property of chords in a circle. According to the property, if two chords of a circle are equidistant from the center, then the lengths of the chords will be equal.
Let's break down the given information:
- The first chord has a length of 10 cm and is at a distance of 8.0 cm from the center.
- The second chord has a length of 8 cm and is at a distance of 3.5 cm from the center.
First, let's check if the two chords are equidistant from the center:
If two points are equidistant from the center of a circle, then the line segment joining the points will be a diameter of the circle.
Since the two distances provided (8.0 cm and 3.5 cm) are not equal, we can conclude that the two chords are not equidistant from the center of the circle. Therefore, it is false to say that the lengths of the chords are 10 cm and 8 cm.
Hence, the statement is false.
Draw a diagram. The half-chords are legs of right triangles, with the radius as hypotenuse. The two triangles require that
r^2 = 4^2 + 3.5^2
r^2 = 8^2 + 5^2
Clearly the two values do not agree, so the assertion is false.