There are two points in one line and a point C which doesn't lie on the line AB. I have to construct a point D such that it is intersection of the line AB and a line which is perpendicular to the line AB and points C and D lies on this perpendicular line.
I can only use compass and can't link (match) the points.
It's on the picture.
Thanks for any help.
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Pls2
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What is the purpose of the point C? – Joey Zou Dec 24 '15 at 00:24
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Please could you be so kind and remove "on hold" from this question? – Pls2 Dec 24 '15 at 10:38
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- construct mirror image of $C$ with respect to line $AB$, let me call it $C'$. 2) construct mirror image of $A$ with respect to line $CC'$, let me call it $A'$. 3) construct mid point of $A$ and $A'$ using method described in this answer, this will be the point $D$ you seek.
– achille hui Dec 24 '15 at 16:55
1 Answers
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Following is a construction based on the method described in this
answer.
At the end is a picture illustrating the configuration/construction.
- Construct two circles (in red) passing through $C$ centered at $A$ and $B$ respectively.
These two circles intersect at $C$ and another point $D$. - Construct a circle (in orange) centered at $C$ passing through $D$.
- Construct a circle (in green) centered at $D$ passing through $C$.
- Start from $D$, following the method of constructing a regular hexagon.
After two more circles, one find the point $E$ on the orange circle antipodal to $D$. - Construct a circle (in blue) centered at $E$ passing through $D$.
This circle intersect the green circle at two points $F$ and $G$. - Construct two circles (in magenta) through $D$ centered at $F$ and $G$
respectively.
They intersect at $D$ and another point $H$.
We have construct totally nine circles. The final point $H$ is lying on line $AB$ and line $CH$ is perpendicular to $AB$. i.e. $H$ is the point we seek.
achille hui
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