logistic_guy
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Describe the error in the diagram of \(\displaystyle \text{\large$\odot$}C\). Find two ways to correct the error.
error
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The Highlander
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If this is a sketch then the only criticism I would have of it is that it is not at all clear what the "100°" refers to and one would need to know what it did refer to before being able to suggest any correction(s).Describe the error in the diagram of \(\displaystyle \text{\large$\odot$}C\). Find two ways to correct the error.
I presume the red lines to the right are just someone marking the sketch "wrong" so they may be disregarded completely.
If C is the centre of the circle then QR is a diameter and thus, if the measure of ∠SQR is 45° (as it is clearly indicated to be), then ΔQRS is a right-angled, isosceles triangle.
QS may not "look" like it is the same length as RS but that's perfectly OK in a sketch; enough information is provided for anyone (with a minimal competence in Geometry) to know that ΔQRS is a right-angled, isosceles triangle from the information that is provided.
Hope that helps.
logistic_guy
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Dear the Highlander,
Take this advice from an expert in diagrams: When you see a sketch or anything similar, always remember this \(\displaystyle \rightarrow \ \textcolor{red}{\bold{Not \ to \ Scale}}\). The key idea of this problem is that it is based on assumption.
If we assume that the angle \(\displaystyle \angle\text{SQR} = \textcolor{green}{\bold{45}^{\circ}}\), then \(\displaystyle \overset{\large\frown}{QS} \neq \textcolor{green}{\bold{100}^{\circ}}\).
If the angle \(\displaystyle \angle\text{SQR} = \textcolor{green}{\bold{45}^{\circ}}\), with the help of \(\displaystyle \textcolor{blue}{\large\text{Inscribed Angle Theorem}}\), we know that \(\displaystyle \overset{\large\frown}{RS} = \textcolor{green}{\bold{90}^{\circ}} = \overset{\large\frown}{QS}\) as \(\displaystyle \overset{\large\frown}{QSR}\) must be \(\displaystyle \textcolor{indigo}{\bold{180}^{\circ}}\).
The second way to correct the error is to assume that \(\displaystyle \overset{\large\frown}{QS} = \textcolor{green}{\bold{100}^{\circ}}\).
\(\displaystyle \textcolor{pink}{\huge\text{Hope that helps}.}\)
Take this advice from an expert in diagrams: When you see a sketch or anything similar, always remember this \(\displaystyle \rightarrow \ \textcolor{red}{\bold{Not \ to \ Scale}}\). The key idea of this problem is that it is based on assumption.
If we assume that the angle \(\displaystyle \angle\text{SQR} = \textcolor{green}{\bold{45}^{\circ}}\), then \(\displaystyle \overset{\large\frown}{QS} \neq \textcolor{green}{\bold{100}^{\circ}}\).
If the angle \(\displaystyle \angle\text{SQR} = \textcolor{green}{\bold{45}^{\circ}}\), with the help of \(\displaystyle \textcolor{blue}{\large\text{Inscribed Angle Theorem}}\), we know that \(\displaystyle \overset{\large\frown}{RS} = \textcolor{green}{\bold{90}^{\circ}} = \overset{\large\frown}{QS}\) as \(\displaystyle \overset{\large\frown}{QSR}\) must be \(\displaystyle \textcolor{indigo}{\bold{180}^{\circ}}\).
The second way to correct the error is to assume that \(\displaystyle \overset{\large\frown}{QS} = \textcolor{green}{\bold{100}^{\circ}}\).
\(\displaystyle \textcolor{pink}{\huge\text{Hope that helps}.}\)