Construct angle QPR line PR=6.5cm RQ=7cm and angle QPR=70degrees drae a ciclr touching three sides of triangle measure radius
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draw PQ
with R as center, draw a circle of radius 7
Construct angle QPR (use protractor)
Where the ray intersects the circle is Q
Now, the circumcenter is the intersection of the angle bisectors of triangle QPR.
To construct a circle touching all three sides of a triangle, we will make use of the fact that the center of this circle lies at the intersection of the three perpendicular bisectors of the triangle's sides. Here are the steps to construct this circle:
1. Draw a line segment PR = 6.5 cm, and another line segment RQ = 7 cm. Place the line segment PR horizontally as the base, and line segment RQ upwards from point R, making an angle of 70 degrees with PR. This gives us triangle PQR.
2. Bisect line segment PR by drawing a perpendicular from point P to intersect PR at point M. Similarly, bisect line segment RQ by drawing a perpendicular from point R to intersect RQ at point N.
3. With a compass, make sure it is set slightly longer than half the distance between PR and RQ (the length of MN). From point M, draw an arc that intersects line segment PR on both sides. From point N, draw an arc that intersects line segment RQ on both sides.
4. Without changing the compass width, place the compass point on point R and draw another arc that intersects the previously drawn arc from step 3.
5. With the compass still set at the same width, move the compass point to the intersection of the arcs drawn in step 3. Draw another arc that intersects the previously drawn arc from step 4.
6. Repeat steps 4 and 5, but this time, place the compass point on point P and draw arcs that intersect the original arc already drawn.
7. Finally, draw a line segment joining the two points where the arcs from step 6 intersect the arc from step 4. This line segment is the perpendicular bisector of segment PQ.
8. Now, repeat steps 1-7 for line segment PQ to obtain the perpendicular bisector of segment QR.
9. The intersection point of the perpendicular bisectors is the center of the circle that touches all three sides of the triangle. Mark this point as center O.
10. Use a compass with the radius equal to the distance between O and any vertex of the triangle (e.g., OP). Draw a circle centered at O.
11. This circle will touch all three sides of the triangle, and the radius of the circle will be the same as the distance between O and any side of the triangle.
Note: This construction assumes that it is possible to construct a circle that touches all three sides of the triangle. In some cases, it may not be geometrically possible.