Using a ruler and a pair of compasses only, construct triangle ABC such that |AB|=8cm, <ABC=60°and <BAC=75°.
i.) Locate the point O inside the ∆ABC equidistant from A,B and C.
ii.) Construct the circle with centre O, which passes through A.
Measure i.)|OA|.
ii.)<ACB.
To construct triangle ABC using a ruler and compasses, follow these steps:
Step 1: Draw a straight line segment AB with a length of 8cm. This will be the base of your triangle.
Step 2: Use a compass to draw an arc with center A and a radius of your choice. This arc will intersect with AB at point C. Label point C.
Step 3: Set the compass width to a distance greater than half the length of AB. Place the compass at point C and draw an arc that intersects with the arc drawn in Step 2. Label this point of intersection as point D.
Step 4: Use a ruler to draw a straight line from point D to point A. This line will be one of the sides of the triangle.
Step 5: Place the compass at point A and draw an arc with a radius that intersects line DA at point E. Label point E.
Step 6: Using a ruler, draw a straight line from point E to point C. This line will be the second side of the triangle.
Step 7: Using a ruler and compass, bisect the angle formed by lines CA and DA. This will give you the third side of the triangle, forming triangle ABC.
To locate point O inside triangle ABC equidistant from A, B, and C:
Step 8: Draw a line segment from point A to the midpoint of line segment BC. Label the midpoint as point M.
Step 9: Using a compass, measure the distance from point A to point M.
To construct a circle with center O that passes through A:
Step 10: Place the compass at point M and draw a circle that passes through point A. This circle will intersect with line segment AB at two points. Label one of the points as point P.
To measure |OA|:
Step 11: Using a ruler, measure the distance from point O to point A.
To measure <ACB:
Step 12: Measure the angle formed by lines AC and BA using a protractor.