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(Q1) Given: ΔABC; ray DB→ is the perpendicular bisector of AC¯;AB=12 inWhat is the length of CB¯ ?By what Theorem?

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Final answer:

To find the length of CB¯, you can use the Pythagorean Theorem. Solve the equation (2x)2 = 122 + x2 to find the value of x. The length of CB¯ is 12 units.

Step-by-step explanation:

To find the length of CB¯, we can use the Pythagorean Theorem. Since ray DB→ is the perpendicular bisector of AC¯, we know that triangle ABC is a right triangle.

Let's denote CB¯ as x. We have AB¯ = 12 and AC¯ = 2x.

By the Pythagorean Theorem, we have (2x)2 = AB¯2 + CB¯2. Substituting the given values, we get (2x)2 = 122 + x2.

Simplifying this equation will give us the value of x, which is the length of CB¯. By rearranging the equation, we have x2 - 144 = 0. Solving this quadratic equation, we find two possible values for x: x = 12 or x = -12. However, since we are dealing with lengths, we take the positive value, so the length of CB¯ is 12 units.

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