7. In circle M, secants PAMD and PBC are drawn from point P such that mBC =100' and mCD = 62'. Which of the following is the measure of ZP? (1) 19* (2) 22" (3) 34" (4) 40°

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Problem 7:**

In circle \( M \), secants \( \overline{PAMD} \) and \( \overline{PBC} \) are drawn from point \( P \) such that \( m\overset{\frown}{BC} = 100^\circ \) and \( m\overset{\frown}{CD} = 62^\circ \). Which of the following is the measure of \( \angle P \)?

1. \( 19^\circ \)
2. \( 22^\circ \)
3. \( 34^\circ \)
4. \( 40^\circ \)

**Explanation of the Diagram:**
- The diagram is of a circle labeled \( M \).
- There are two secant lines intersecting the circle at points \( A, B, C \), and \( D \).
- Secant \( \overline{PAMD} \) intersects the circle at points \( A \) and \( D \).
- Secant \( \overline{PBC} \) intersects the circle at points \( B \) and \( C \).
- The measure of arc \( \overset{\frown}{BC} \) is \( 100^\circ \), and the measure of arc \( \overset{\frown}{CD} \) is \( 62^\circ \).

**To Determine:**
The measure of \( \angle P \).
Transcribed Image Text:**Problem 7:** In circle \( M \), secants \( \overline{PAMD} \) and \( \overline{PBC} \) are drawn from point \( P \) such that \( m\overset{\frown}{BC} = 100^\circ \) and \( m\overset{\frown}{CD} = 62^\circ \). Which of the following is the measure of \( \angle P \)? 1. \( 19^\circ \) 2. \( 22^\circ \) 3. \( 34^\circ \) 4. \( 40^\circ \) **Explanation of the Diagram:** - The diagram is of a circle labeled \( M \). - There are two secant lines intersecting the circle at points \( A, B, C \), and \( D \). - Secant \( \overline{PAMD} \) intersects the circle at points \( A \) and \( D \). - Secant \( \overline{PBC} \) intersects the circle at points \( B \) and \( C \). - The measure of arc \( \overset{\frown}{BC} \) is \( 100^\circ \), and the measure of arc \( \overset{\frown}{CD} \) is \( 62^\circ \). **To Determine:** The measure of \( \angle P \).
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