triangle ABC,angleA=60 degree,angleB=70 degree,angleC=50 degree. AB=6cm,BC=6.5cm,AC=7cm. Find its incentre.
if you are looking for the radius...
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You are given A, B, C and a,b,c
To find the incenter of triangle ABC, we need to find the intersection of the three angle bisectors. The incenter is the point equidistant from all three sides of the triangle. Here's how you can find the incenter:
1. Draw triangle ABC and label the given angles and side lengths.
2. Construct the angle bisectors of angles A, B, and C. An angle bisector divides an angle into two equal angles. To construct an angle bisector, you can use a compass and a straightedge. Start by drawing any two rays from the vertex of the angle. With the compass, draw arcs on each ray that intersect both sides of the angle. Draw a straight line through the point where the arcs intersect, and this line will bisect the angle.
3. Label the points where the angle bisectors intersect the opposite sides of the triangle. Let's call these points D, E, and F.
4. The intersection point of the angle bisectors, which is the incenter, is the point of concurrency of lines AD, BE, and CF. Let's call this point I.
5. To find the exact location of the incenter, construct the perpendicular bisectors of any two sides of the triangle. A perpendicular bisector is a line that divides a side into two equal segments at a 90-degree angle. To construct a perpendicular bisector, use a compass and a straightedge. Start by drawing a circle with the center at one end of the side and the radius equal to the length of the side. Repeat this process for the other end of the side. The point where the circles intersect is the midpoint of the side. Draw a straight line through the midpoint, and this line will be the perpendicular bisector.
6. Label the midpoint of AB as M and the midpoint of BC as N.
7. The intersection of lines MN and DE is the center of the circle inscribed within the triangle, which is the incenter. Let's call this point G.
8. Now, draw a circle with point G as the center and a radius equal to the distance between G and any vertex of the triangle. This circle will be tangent to all three sides of the triangle.
9. The point G is the incenter of triangle ABC.
By following these steps, you should be able to find the incenter of triangle ABC.