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Find Angle ANB = Angle AOB = Angle AMB=?

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Last updated date: 22nd Feb 2024
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IVSAT 2024
Answer
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Hint: In order to solve the given question , we will be using the theorem which states that the angle subtended by an arc at the center is double the angle subtended by it on any point on the remaining part of the circle .

Complete step-by-step answer:
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Let us consider the angle ANB first , we can see in the image , AB is the diameter .
Therefore, the angle subtended by the arc AB at the centre is ${180^ \circ }$. Give the centre a name like X.
So, $\angle AXB = {180^ \circ }$ . Using the theorem which states that the angle subtended by an arc at the center is double the angle subtended by it on any point on the remaining part of the circle .
$\angle AXB = 2\angle ANB$
$\angle ANB$is the angle made at any point on the circle .
\[
  \angle AXB = 2\angle ANB \\
  \dfrac{{\angle AXB}}{2} = \angle ANB \\
  \dfrac{{{{180}^ \circ }}}{2} = \angle ANB \\
  \angle ANB = {90^ \circ } \;
 \]
Similarly , it can be said that angle inscribed in a semicircle is a right angle so Angle ANB = Angle AOB = Angle AMB=${90^ \circ }$, because like \[\angle ANB = {90^ \circ }\],$\angle AOB,\angle AMB$are also the angles made at any point on the circle .
So, the correct answer is “\[{90^ \circ }\]”.

Note: An arc of a circle is any portion of the circumference of a circle. To recall, the circumference of a circle is the perimeter or distance around a circle. Therefore, we can say that the circumference of a circle is the full arc of the circle itself.