Prove that MN ext is parallel to AP.

May 21, 2026Mathematics

ScanSolve AI Answer

May 21, 2026

Answer

$\angle APB = 90^\circ$ , which means $AP \perp PB$

Here's a step-by-step solution for Question 5:

5.1 Prove that $MN \parallel AP$

Step 1: Identify perpendicular lines. AB is the diameter of the circle, so the angle subtended by the diameter at any point on the circumference is $90^\circ$ . Therefore, $\angle APB = 90^\circ$ , which means $AP \perp PB$ . We are given that $MN$ is perpendicular to $PB$ . So, $MN \perp PB$ .

Step 2: Conclude parallelism. Since both line segment $AP$ and line segment $MN$ are perpendicular to the same line segment $PB$ , they must be parallel to each other. Therefore, $MN \parallel AP$ .

**5

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Here's a step-by-step solution for Question 5: 5.1 Prove that MN AP Step 1: Identify perpendicular lines.

Asked on May 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 21, 2026

Here's a step-by-step solution for Question 5: 5.1 Prove that MN AP Step 1: Identify perpendicular lines. AB is the diameter of the circle, so the angle subtended by the diameter at any point on the circumference is 90^. Therefore, APB = 90^, which means AP PB. We are given that MN is perpendicular to PB. So, MN PB. Step 2: Conclude parallelism. Since both line segment AP and line segment MN are perpendicular to the same line segment PB, they must be parallel to each other. Therefore, MN AP. **5