Before watching the video the only things that I knew about was that I knew what a secant and a tangent were. There is nothing else that I knew about before watching the video.
After watching the video I learned about three different theorems. The first one is the chord intersection theorem. The chord intersection theorem is if two chords intersect in the interior of a circle, then the product of the segments of one chord equals the product of the other segments. If secant CD and secant AB intersect in the same spot in circle E, then you have EA multiplied by EB equals EC multiplied by ED. The second/third theorems are the external secant and tangent theorems. The second one deals with secants and secants and the third one deals with secants and tangents. So, the secant and secant theorem is if two secants share the same endpoint outside a circle, then the products of the external segment and the whole segment equals the other product of the external and whole segment. So, if secant AB and secant CD have the same endpoint outside of the circle, which is point E, then EA multiplied by EB equals EC multiplied by ED. The last theorem is the secant and tangent theorem. That is if a secant and a tangent share an endpoint outside a circle, then the tangent segment squared equals the product of the external and internal segments of the secant. So, if tangent EA and secant ED share the same endpoint outside the circle, which is point E, then EA squared equals EC multiplied by ED. This is everything that I learned about after watching the video.
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For your 1st question we would sue the External secant and tangent theorem, which states that if a secant and a tangent segment share the same endpoint on the outside of a circle then those segments ^2 = the product of the external and internal segments of the secant. In this case we would have x^2= 20*45.Then we would have x^2 =900. Then we would take the square root of both sides and find that x=30, or the letter D.
ReplyDeleteI agree with what you have written about this lecture. I will answer your first question. You first know that because MN is tangent to the circle, x would be times its self so it would then be x^2. For the other segment, it is 20 times 45. You get 45 because it is the outside segment times the whole segment. You would then get x^2=900. Once you square root it you get your answer as 30.
ReplyDeleteYour second question I think I put as a question too because I was really confused when I was watching that on the lecture, so I'm going to attempt problem 1! So we know that segment MN is the tangent to the circle therefore we would have x squared using our equations to refer back too and then the other segment on the other side we have to take 45 which is the whole segment multiplied together with 20 which is only part of the segment. So then we have that to equal 900 and set that equal to x squared from before and the square root of x squared is x and 900 is 30 so our answer is 30.
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