To find the diameter of the wheel, we can use the Intersecting Chords Theorem, which states that when two chords intersect in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
From the given lengths:
IM = 16 cm
MJ = 7 cm
LM = 4 cm
MK = x
Using the Intersecting Chords Theorem, we can write the equation as:
IM * MJ = LM * MK
16 * 7 = 4 * x
112 = 4x
x = 28cm
Since LK goes through the center of the wheel, MK is the diameter of the wheel.
Therefore, the diameter of the wheel is 28 cm.
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
.
1 answer
1 answer