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Question

A circle has center point upper A. Points upper C and upper D are plotted on the circumference of the circle. Point upper B lies outside the circle. Tangent segments join points upper C and upper D with upper B.

If arc CD=73
degrees, then what is the measure of ∠B
?

(1 point)
degrees
Remaining Attempts : 3

Answer 1

To find the measure of angle ∠B, we can use the properties of circles and tangents. When two tangent segments are drawn from an external point to points on the circle, the angle formed between the two tangent segments and the line connecting the external point to the center of the circle has a specific relationship with the arc subtended by the points on the circle.

In this case, the measure of angle ∠B, which is the angle between the tangent segments BC and BD, is related to the measure of the arc CD that is intercepted by those tangent segments.

The measure of angle ∠B can be calculated using the following formula: \[ \angle B = \frac{1}{2} \times \text{measure of arc } CD \] Given that the measure of arc CD = 73 degrees, we can substitute this value into the formula:

\[ \angle B = \frac{1}{2} \times 73 = 36.5 \text{ degrees} \]

So the measure of ∠B is: \[ \angle B = 36.5 \text{ degrees} \]