Prove the equal tangent theorem: Let P be a point outside a circle C. Let A be a point on C such that PA is tangent to C. Let B be the other such point on C. Then PA = PB. (You may assume that the angle between a radius of a circle and the tangent to the circle at the end-point of the radius is a right angle.)

Q: Consider the gridlines in this plot to be 5 units apart.   sin(θ) = cos(ϕ) = tan(θ) = tan(ϕ) =

A: We name the triangle ABC.

Q: Make a diagram of the unit circle with an angle e in QI and its supplement 180° - e in QII. Label…

A: I am attaching image so that you understand each and every step.

Q: The two lines are tangent as they appear. Find angle x 105° O Find

A: By using circle property, we find the value of 'x'.

Q: Find an angle θ such that 0 < θ < 2 π and θ has the same circle point as 8 π/  3.

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Q: Consider the unit circle x² + y² =1 and the point P(1,0). Find the average distance from P to a…

A: The  average distance betwwen point and circle is zero  it shows that the point lies on the circle…

Q: To construct the tangent to circle O, at point T on the circle, we construct a line perpendicular to…

A: To construct the tangent to circle O, at point T on the circle, we construct a line perpendicular to…

Q: 1. Line AB is tangent to circle O at A. If AB = 12 and OA = 5, find OB %3D B.

A: We have to find OB

Q: An ant looks up at a UFO at an angle of elevation of 23 degrees. The ant noticed that the shadow of…

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Q: Let A = (0,0), B = (4,0), and C = (4,3). Mark point D so that ACD is a right angle and DAC is a…

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Q: 1.)  Two circles that are internally tangent have three common tangent lines. A. True     b.False…

A: Given problems:- 1.) Two circles that are internally tangent have three common tangent lines.   A.…

Q: Find all values of x where the tangent lines to y = x and y = x° are parallel.

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Q: KS. (a) Give a tangent line. (b) Give a secant line. C (c) Give a chord. K H

A: (a)  Tangent to a circle is the line that touches the circle at only one point. From figure we can…

Q: 8 10 Y

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Q: Determine if angle X & Y is tangent to circle Z

A: XY is a tangent of the circle Z if the triangle XYZ is a right angle triangle and angle X is a 90…