Question

A bike wheel is shown. Chords I J and L K intersect at point M. The length of I M is 16 centimeters, the length of M J is 7 centimeters, the length of L M is 4 centimeters, and the length of M K is x. LK goes through the center of the wheel pictured. Find the diameter of the wheel. Use the intersecting chords theorem to write the equation . The diameter of the wheel is .

The first drop down is 4x=(7)(16)
The second drop down is 32

Answer 1

4x=(7)(16)

the diameter of the wheel is 32cm

Explanation:

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Answer 2

The diameter of the wheel is 32 centimeters

Explanation:

we know that

The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal.

so

In this problem

`(LM)(MK)=(IM)(MJ)`

substitute the given values

`(4)(x)=(16)(7)`

solve for x

`x=16(7)/4\\x=28\ cm`

Remember that

LK goes through the center of the wheel

That means----> LK is a diameter

`LK=4+x\\LK=4+28=32\ cm`

therefore

The diameter of the wheel is 32 centimeters