In Exercises 9 and 10, point D is a point of tangency. 9. Find BD. 10. Point C is also a point of tangency. If BC = 4x + 6, find the value of x to the nearest tenth. A. 5.5 D 10

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**Geometry Practice Problems**

In Exercises 9 and 10, point D is a point of tangency.

**9.** Find \(BD\).

**10.** Point C is also a point of tangency. If \(BC = 4x + 6\), find the value of \(x\) to the nearest tenth.

---

A diagram is provided below for reference:

- There is a circle with center \(A\) and a radius of 5.5 units.
- A line tangential to point \(D\) on the circle extends outwards, labeled as segment \(BD\).
- Another tangent line touches the circle at point \(C\).
- The tangents \(BD\) and \(BC\) intersect at point \(B\), which is outside the circle.
- The length of \(A\) to \(B\) (noted as \(AB\)) is given as 10 units.

---

**Extra Practice:** p534: 1-26, 29-34

---

**Graph/Diagram Explanation:**

1. **Circle** - There is a circle centered at point \(A\) with a radius of 5.5 units.
2. **Tangents** - Two tangents originate from point \(B\) outside the circle and touch the circle at points \(D\) and \(C\), respectively.
3. **Length \(AB\)** - The distance provided from \(A\) to \(B\) is 10 units.
4. **Equation** - The segment \(BC\) is expressed as \(4x + 6\).

The task requires determining the length of the segment \(BD\) and solving for \(x\) in the equation for \(BC\).
Transcribed Image Text:**Geometry Practice Problems** In Exercises 9 and 10, point D is a point of tangency. **9.** Find \(BD\). **10.** Point C is also a point of tangency. If \(BC = 4x + 6\), find the value of \(x\) to the nearest tenth. --- A diagram is provided below for reference: - There is a circle with center \(A\) and a radius of 5.5 units. - A line tangential to point \(D\) on the circle extends outwards, labeled as segment \(BD\). - Another tangent line touches the circle at point \(C\). - The tangents \(BD\) and \(BC\) intersect at point \(B\), which is outside the circle. - The length of \(A\) to \(B\) (noted as \(AB\)) is given as 10 units. --- **Extra Practice:** p534: 1-26, 29-34 --- **Graph/Diagram Explanation:** 1. **Circle** - There is a circle centered at point \(A\) with a radius of 5.5 units. 2. **Tangents** - Two tangents originate from point \(B\) outside the circle and touch the circle at points \(D\) and \(C\), respectively. 3. **Length \(AB\)** - The distance provided from \(A\) to \(B\) is 10 units. 4. **Equation** - The segment \(BC\) is expressed as \(4x + 6\). The task requires determining the length of the segment \(BD\) and solving for \(x\) in the equation for \(BC\).
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