Using a ruler and a pair of compasses only construct triangle ABC such that AB=8cm,angle ABC=60degree and angle BAC =75degree,Locate the point O inside triangle ABC equidistant from A,B and C. Construct the circle with center O, which passes through A.Measure OA and angle ACD
where is D?
and O is the circumcenter of ABC.
You can read online how to find it.
lil besh
Yes
To construct triangle ABC:
1. Using the ruler, draw a line segment AB with a length of 8 cm.
2. Place the compass at point A, and set the width of the compass to a random length.
3. Draw an arc from point B above the line, intersecting the line segment AB.
4. Without changing the compass width, place the compass at point B and draw another arc, intersecting the previous arc drawn.
5. Mark the intersection point as C.
Triangle ABC is now constructed.
Now, to locate the point O inside triangle ABC, equidistant from A, B, and C:
1. Draw the perpendicular bisectors of line segments AB, AC, and BC using the compass and ruler.
2. Place the compass on the intersection point of the perpendicular bisectors of line segments AB and BC.
3. Draw an arc with the compass to create a circle passing through points A, B, and C.
The point O is the center of this circle.
To measure OA and angle ACD:
1. Place the compass on point O and measure the distance to point A. This will give you the length OA.
2. To measure angle ACD, place the compass on point C and draw an arc that intersects the line segment AD (where D is the intersection point of line segment AC and the circle).
3. Now, measure the angle between line segment CD and line segment AC using a protractor.
By following these construction steps, you should be able to construct triangle ABC and find the point O, as well as measure OA and angle ACD.