if i put three points on the common arm ,then they are common points for both the two angles
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Yes. Draw three line segments so that they cross at three points forming a triangle (with each side extending beyond the vertices of the triangle). Draw one circle to enclose the triangle without touching it to intersect the extended sides at a further 6 points, making 9 points of intersection so far. Draw the second circle slightly shifted (relative to the first) so that it also encloses the triangle (without touching it) creating a further 6 intersection points with the three lines and 2 with the first circle; an additional 8 intersection points making 17 in all.
You cannot.
Yes it is. A normal, 3:4:5 triangle has a right angle, three different angles, and three different sides. There should be more for you to find.
Draw a pair of lines, AB and BC meeting at a right angle at B. Pick another two points, D and E in the plane. Join CD, DE and EA. If any of the angles other than at B is a right angle, you can fix it by moving one of the points D or E.
Yes you can. The problem is on what surface you draw the triangle. On a plane this would be impossible, but if you do it on a spherical surface then you can even draw a triangle with 3 right angles.