Given that angle ADB, which is 69\degree, is the angle between the side of the triangle and the tangent, then the alternate segment theorem immediately gives us that the opposite interior angle, angle AED (the one we’re looking for), is also 69\degree. 6 Answers Sorted by: 17 For your first question Point C in your diagram above is simple, just ( cx, cy + r ). Also, note that since triangle AOB is isosceles. This tells us that the angle between the tangent and the side of the triangle is equal to the opposite interior angle. then OAOB, therefore this forms an isosceles triangle inside the circle. Now we can use our second circle theorem, this time the alternate segment theorem. Let the size of one of these angles be x, then using the fact that angles in a triangle add to 180, we get Move one or more of the points C, D, E, until you have a right triangle (one of the angles is 90 degrees.) What do you notice. In this case those two angles are angles BAD and ADB, neither of which know. This means that ABD must be an isosceles triangle, and so the two angles at the base must be equal. Our first circle theorem here will be: tangents to a circle from the same point are equal, which in this case tells us that AB and BD are equal in length.
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