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In the figure below is tangent to circle at , , and . Find
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Q. In the figure below is tangent to circle at , , and . Find
- Identify Theorem: Identify the relevant theorem for solving the problem. Since is tangent to the circle at , and we know , we can use the Pythagorean theorem in triangle , assuming is the hypotenuse.
- Set Up Pythagorean Theorem: Set up the Pythagorean theorem for triangle ADB. Let AB = x, then:We need to find BD, which is the radius of the circle.
- Use Pythagorean Theorem: Since BC = and it is a chord, the perpendicular from the center O to BC (let's call it OM) bisects BC. So, BM = MC = . Using the Pythagorean theorem in triangle OMB (right triangle), where OM is the radius:This equation is incorrect, as it implies that ^ = .
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