12. Find the value of x for m48-46 and CD-25. (The figure is not drawn to scale.) D B A. 35.5 B. 58.5 C. 71 D. 21 13. DA is tangent to the circle at A and DC is tangent to the circle at C. Find m2D for m2B-56. (The figure is not drawn to scale.)

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Chapter2: Second-order Linear Odes
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12,13, and 14 as per Bartleby guidelines the first three are answered
Certainly! Below is the transcription of the image with detailed explanations of the diagrams presented.

---

## Geometry Problems and Solutions

### Problem 12:
Find the value of \(x\) for \(m\overset{\frown}{AB} = 46\) and \(m\overset{\frown}{CD} = 25\). (The figure is not drawn to scale.)

**Diagram Explanation:**
This problem features a circle with center \(O\). The circle is intersected by two chords, \(AB\) and \(CD\). The measure of arc \(AB\) is given as \(46\) degrees, and the measure of arc \(CD\) is given as \(25\) degrees. The chords intersect at a point within the circle, with the point of intersection labeled as \(X\).

**Answer Choices:**
- A. 35.5
- B. 58.5
- C. 71
- D. 21

---

### Problem 13:
\( \overline{DA} \) is tangent to the circle at \(A\) and \( \overline{DC} \) is tangent to the circle at \(C\). Find \( m\angle D \) for \( m\angle B = 56 \). (The figure is not drawn to scale.)

**Diagram Explanation:**
This diagram features a circle with center \(O\). From points \(A\) and \(C\) on the circle, tangents \( \overline{DA} \) and \( \overline{DC} \) extend outward, meeting at point \(D\) outside the circle. There is also a chord \( \overline{BC} \) within the circle. The given measure of angle \(B\) is \(56\) degrees.

**Answer Choices:**
- A. 136
- B. 124
- C. 68
- D. 62

---

### Problem 14:
A park maintenance person stands \(16\) m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of \(56\degree\). What is the measure of the arc of the monument that her lines of sight intersect?

**Answer Choices:**
- A. 124
- B. 248
- C. 112
- D. 28

**Note:** There is
Transcribed Image Text:Certainly! Below is the transcription of the image with detailed explanations of the diagrams presented. --- ## Geometry Problems and Solutions ### Problem 12: Find the value of \(x\) for \(m\overset{\frown}{AB} = 46\) and \(m\overset{\frown}{CD} = 25\). (The figure is not drawn to scale.) **Diagram Explanation:** This problem features a circle with center \(O\). The circle is intersected by two chords, \(AB\) and \(CD\). The measure of arc \(AB\) is given as \(46\) degrees, and the measure of arc \(CD\) is given as \(25\) degrees. The chords intersect at a point within the circle, with the point of intersection labeled as \(X\). **Answer Choices:** - A. 35.5 - B. 58.5 - C. 71 - D. 21 --- ### Problem 13: \( \overline{DA} \) is tangent to the circle at \(A\) and \( \overline{DC} \) is tangent to the circle at \(C\). Find \( m\angle D \) for \( m\angle B = 56 \). (The figure is not drawn to scale.) **Diagram Explanation:** This diagram features a circle with center \(O\). From points \(A\) and \(C\) on the circle, tangents \( \overline{DA} \) and \( \overline{DC} \) extend outward, meeting at point \(D\) outside the circle. There is also a chord \( \overline{BC} \) within the circle. The given measure of angle \(B\) is \(56\) degrees. **Answer Choices:** - A. 136 - B. 124 - C. 68 - D. 62 --- ### Problem 14: A park maintenance person stands \(16\) m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of \(56\degree\). What is the measure of the arc of the monument that her lines of sight intersect? **Answer Choices:** - A. 124 - B. 248 - C. 112 - D. 28 **Note:** There is
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