Radius OA of circle O has a slope of 2.5. What is the slope of the line tangent to circle O to point A?
2 answers:
Answer: The required slope of the line tangent to the circle at point A is -0.4.
Step-by-step explanation: Given that the radius OA of a circle with center O has a slope of 2.5.
We are to find the slope of the line tangent to the circle at the point A.
We know that
The radius of a circle at a point on the circumference of a circle is perpendicular to the tangent line at the same point on the circumference of the circle.
Also, the product of the slopes of two perpendicular lines is -1.
So, if m is the slope of the tangent line at the point A, then we must have
Thus, the required slope of the line tangent to the circle at point A is -0.4.
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Answer: D) 300 degrees (counterclockwise)
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We want to have segment PQ rotate around the center so that it lines up with segment RF. Put another way: we want point P to rotate around the center to have it line up with point R, and we want Q to rotate so that it moves to point F.
Going clockwise, this is a rotation of 60 degrees as the diagram below shows (each blue arc is 30 degrees, so in total it's 30+30 = 60). In that diagram, I'm only focusing on moving point P. Point Q moves in a similar fashion. Since 60 is not an answer, this means 360-60 = 300 must be the answer.
