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RT is tangent to circle S at point T. if UR=14, and ST=8, find RT

RT is tangent to circle S at point T. if UR=14, and ST=8, find RT-example-1
User Ehsavoie
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answer: C, 2√105

explanation: because we have our known measurements of the radius st=8, and ru=14, we can substitute 8 for us because it is also a radius. Thus rs=22. Because of the radii formed and tangent rt a right angle is formed which means that we can use the Pythagorean theorem because it is a right triangle, and enough variables are known to solve. Using the Pythagorean theorem a^2+b^2=c^2, we can rearrange this to b^2=c^2-a^2 to solve for x. When we plug this in, we get that 22^2-8^2=x, √484-64=√420=2√105

User Swoox
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