Question

What is the length of the longer of the two chords shown?
Length of longer chord= ? units

Answer 1

Length of the chord= 19units

Explanation:

It is given from the figure that there is a circle with center C and two chords are intersecting each other, and we know that when two chords of the circle intersect each other then the product of their segments are equal, thus

`4(x+3)=12(x-7)`

`4x+12=12x-84`

`12+84=12x-4x`

`96=8x`

`x=12`

Thus, the value of the chords are:

`4+x+3=4+12+3=19` and
`12+x-7=12+12-7=17`

Thus, the length of the larger chord is
`4+x+3=4+12+3=19` .