Question

In circle O, BC=14 and DC=25. What is the length of diameter BA? -58.6 -12.2 -44.6 -30.6

Answer 1

the picture in the attached figure

we know that
If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
DC²=BC*CA-----> CA=DC²/BC
DC=25
BC=14
CA=25²/14-----> CA=44.64
CA=BC+BA----> BA=CA-BC----> BA=44.64-14----> BA=30.64

BA is the diameter
hence
the length of diameter BA is 30.64----> round to the nearest tenth---> 30.6

the answer is
the length of diameter BA is 30.6

Answer 2

The length of diameter BA of the given cyclic diagram is; 30.6

How to find the diameter of a circle?

From the tangent segment theorem, we know that;

If a tangent segment and a secant segment are drawn to a circle from an exterior point, it means that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

From the image of the first answer, we can find the diameter BA by first getting the length of CA;

CA = DC²/BC

DC = 25

BC = 14

Thus;

CA = 25²/14

CA = 44.64

Thus;

BA = CA - BC

BA = 44.64 - 14

Diameter BA = 30.64

Approximating to the nearest tenth gives;

Diameter BA = 30.6

Read more about Cyclic angles at; https://brainly.com/question/24368895

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