To find the length of the diameter BA, we can use the chord-chord product theorem. This theorem states that for two chords intersecting in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
BC * DC = AC * EC
Substitute the values given for BC and DC:
18 * 42 = AC * EC
756 = AC * EC
Since E is the midpoint of the chord AC, the lengths of AC and EC are equal. Therefore, in this case, EC = AC.
So, EC = AC = √756 = 27.5.
Since the diameter of the circle is twice the length of the radius, we can find the diameter BA:
BA = 2 * AC = 2 * 27.5 = 55
Rounding to the nearest tenth, the length of diameter BA is 55.0.
In circle O, BC = 18 and DC = 42. The diagram is not drawn to scale. What is the length of diameter BA? Round the answer to the nearest tenth. (1 point) Responses 24.3 24.3 80.0 80.0 37.3 37.3 45.5
1 answer
1 answer