for an angle equal to QPM. This is the angle between the tangent MPT and the chord QP at the point of contact P.

Question

for an angle equal to QPM. This is the angle between the tangent MPT and the chord QP at the point of contact P.

Asked on April 20, 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.

Accepted Answer · 2026-04-20T17:21:12.444Z

Step 1: Identify the angle to be found. The question asks for an angle equal to $\angle QPM$. This is the angle between the tangent MPT and the chord QP at the point of contact P. Step 2: Apply the Alternate Segment Theorem. The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. For the tangent MPT and chord QP, the angle $\angle QPM$ is equal to the angle subtended by the chord QP in the alternate segment, which is $\angle QRP$. So, $\angle QPM = \angle QRP$. Step 3: Examine the given options. We need to find an angle from the options that is

for an angle equal to QPM. This is the angle between the tangent MPT and the chord QP at the point of contact P.

for an angle equal to QPM. This is the angle between the tangent MPT and the chord QP at the point of contact P.

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