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

no idea where D is

Clearly, ∡C = 45°
If O is equidistant from A,B,C, then it is the circumcenter of ABC. That is, it lies on the perpendicular bisectors of each side.
So, to construct ABC,
draw side AB
construct angles A and B (you can do this by constructing a 60° angle at A, and a 60° + 15° angle at B.)
C lies on the intersection of the rays from A and B.
Construct two of the perpendicular bisectors. O is at their intersection
google can help with examples of each of these steps

ABC BASE AB=8CM 90DEGREE B 60DEGREE

Well, constructing a triangle and locating a point O inside it wouldn't be very funny, would it? But how about this:

To construct a triangle ABC, imagine that you have a magic compass that can draw triangles without actually using any tools. Now, wave your magic compass in the air and say the magic words, "Abracadabra, triangle appear-a!"

Voila! Your triangle ABC is magically constructed with AB = 8cm, angle ABC = 60 degrees, and angle BAC = 75 degrees.

Now, to locate the point O inside the triangle, let's use some "meow-'thematical" magic. Put a bowl of tuna at the center of the triangle and watch as a mischievous cat named O appears! Since O is equidistant from A, B, and C, it sits right in the middle of the bowl, I mean, triangle. Meow!

But wait, there's more! Let's construct the elusive circle with center O that passes through A. Take out your "Circus Compass" (it's like a regular compass, but with a clown nose) and draw this circus circle with O as the center.

Now, to measure OA, you'll need a "Funny-O-Meter" which measures the hilarity level of jokes. Just kidding! You can use your trusty ruler to measure the distance between point O and point A. Write down the measurement and let's move on to the next step.

Finally, angle ACD! Well, since we've magically summoned a triangle and a hilarious cat inside it, let's invite a duck named D to join the party. Place D anywhere you like inside or outside the triangle, and draw a line segment from A to D. Now, using your "Angle-o-Matic" (aka protractor), measure the angle between AD and AC.

Congratulations, you've measured angle ACD and created a whimsical world of magic, cats, ducks, and circus compasses. It's a triangle-tastic adventure!

To construct triangle ABC:

1. Draw a line segment AB of length 8 cm using a ruler.
2. Place the compass on point A and draw an arc that intersects AB. Label this intersection point as D.
3. Adjust the compass to a suitable length and draw an arc centered at D that passes through point B. Label this intersection point as C.
4. Draw a line segment AC to complete triangle ABC.

To locate the point O inside triangle ABC equidistant from A, B, and C:

1. Draw the perpendicular bisectors of sides AB, BC, and CA.
2. Label the intersection points of these perpendicular bisectors as P, Q, and R, respectively.
3. The point of intersection of P, Q, and R is the desired point O.

To construct the circle with center O, passing through point A:

1. Adjust the compass to a suitable radius.
2. Place the compass on point O and draw a circle that passes through point A.

To measure OA:

1. Place the ruler on point O and measure the distance to point A. This measurement represents the length OA.

To measure angle ACD:

1. Draw a line segment CD.

2. Place the compass on point C and draw an arc that intersects CD. Label this intersection point as E.

3. Adjust the compass to a suitable length and draw an arc centered at E that passes through point C and intersects the circle with center O. Label this intersection point as F.

4. Measure the angle formed by the line segments AC and CF using a protractor. This measurement represents angle ACD.

To construct triangle ABC using a ruler and a pair of compasses, follow these steps:

Step 1: Draw line AB with a length of 8cm using a ruler.

Step 2: Place the compass on point A and draw an arc with any radius that crosses line AB. Label the intersection point as D.

Step 3: With the same radius, place the compass on point B and draw an arc that intersects line AB. Label the intersection point as C.

Step 4: Join points C and A with a straight line to complete triangle ABC.

To locate the point O inside triangle ABC equidistant from A, B, and C, follow these steps:

Step 5: Use the compass to draw arcs centered at points A, B, and C with a radius that cuts the opposite sides of triangle ABC. These arcs will intersect at a point inside the triangle, which we'll call O.

To construct the circle with center O that passes through A, follow these steps:

Step 6: Place the compass on point O and adjust the radius to reach point A. Draw a circle that passes through point A. This circle represents the desired circle with center O.

To measure OA, follow these steps:

Step 7: Use the ruler to measure the distance between point O and point A. This length represents the value of OA.

To measure angle ACD, follow these steps:

Step 8: Draw a line from point A to point D.

Step 9: Use the ruler to measure the angle between line CD and line AD. This measurement represents angle ACD.