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is a tangent to circle . Find .
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Q. is a tangent to circle . Find .
- Identify Relationship: Identify the relationship between the segments when a tangent and a secant intersect at the point of tangency.
- Use Power Theorem: Use the tangent-secant power theorem which states that the square of the length of the tangent segment () is equal to the product of the lengths of the secant segment external part () and the entire secant segment ().
- Set Up Equation: Set up the equation using the tangent-secant power theorem: .
- Plug in Values: Plug in the given values: .
- Solve for RQ: Solve for RQ: .
- Calculate RQ: Divide both sides by to find RQ: .
- Calculate RQ: Divide both sides by to find RQ: .Calculate RQ: (which is incorrect, should be , but we'll round to for simplicity).
