how do i prove that the angle between a tangent and a radius is 90 degrees?
One way is to draw a chord of the circle that is bisected by a radius vector. By similar triangles you can show that the angle between the chord you drew and the radius line is 90 degrees. Then shrink the length of that chord until t just barely cuts the circle.
o great job greg o is it mames im sorry kanes
To prove that the angle between a tangent and a radius is 90 degrees, we need to use basic geometry principles. Here's a step-by-step explanation of how to prove it:
Step 1: Draw a circle with its center at point O. Mark a point A on the circumference of the circle, which will be the point where the tangent line intersects the circle.
Step 2: Draw a radius line from the center O to the point A on the circumference.
Step 3: Now, let's draw the tangent line. A tangent line is a line that only touches the circle at one point and is perpendicular to the radius at that point. Draw a line that originates from point A and touches the circle at point B.
Step 4: To prove that the angle between the tangent line AB and the radius line OA is 90 degrees, we need to show that angle OAB is a right angle.
Step 5: Let's focus on triangle OAB. By definition, a radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circumference. Thus, OA is a radius, and AB is a tangent line.
Step 6: Since OA is a radius line, it is always perpendicular to the circle's circumference at point A. Therefore, angle OAB is a right angle (∠OAB = 90 degrees).
By following these steps, you have shown that the angle between a tangent and a radius on a circle is always 90 degrees.