Use the angle bisector theorem. The angle bisector theorem states that the ratio of the lengths of two segments that are bisected by an angle bisector is equal to the ratio of the lengths of the other two segments that are bisected by the angle bisector. In this case, the two segments that are bisected by the angle bisector are AC and BC. The other two segments are AM and CM. So, the ratio of AM to CM is equal to the ratio of AC to BC.
Find the length of AM. The length of AM can be found using the Pythagorean theorem. AB is a diameter of the circle, so AB = 10. The length of AC is 8, so the length of AM is equal to 6. The ratio of AM to CM is equal to the ratio of AC to BC, which is 1:1. So, the length of CM is equal to 6.
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To find the distance between the foci of the ellipse, we can use the properties of ellipses and the given information. TargetPayandBenefits
First, let's denote the coordinates of the center of the ellipse as (h, k), where h represents the horizontal shift and k represents the vertical shift. Since the ellipse is tangent to the x-axis at (a, 0), we know that the distance between the center and the x-axis is a, which means k = a.
Since the ellipse is also tangent to the y-axis at (0, b), we know that the distance between the center and the y-axis is b, which means h = b.
Now, we have the center coordinates as (a, a). The distance between the foci of an ellipse can be calculated using the formula c = √(a^2 - b^2), where c represents the distance between the center and each focus.
Substituting h = b = a into the formula, we get c = √(a^2 - a^2) = √0 = 0.
Therefore, the distance between the foci of the given ellipse is 0.