12 Using a ruler and a pair of compasses only, construct a a triangle PQR with |PQ|= 10 cm, |PR| = 8 cm and IQRI = 6 cm b a circle centre N to pass through P and touch QR at R c a circle centre M to pass through the vertices of the triangle. Measure /NM/and angle PRQ.
Ответы
Here are the steps to construct the triangle PQR and circles in the problem:
a. Construct the segment PQ of length 10 cm using a ruler.
b. Construct the segment PR of length 8 cm with an angle of 6 degrees between PQ and PR using a protractor and a ruler.
c. Construct the perpendicular bisector of segment QR using a compass and a ruler. The intersection of the perpendicular bisector and QR is the point R.
d. Draw a circle with center N and passing through point P using a compass.
e. Draw a line passing through points P and R using a ruler.
f. Construct the angle bisector of angle PQR using a compass.
g. The intersection of the angle bisector and line PR is point Q.
h. Draw a circle with center M passing through points P, Q, and R using a compass.
To measure /NM/ and angle PRQ, we need to make some additional constructions:
i. Draw a line passing through points N and M.
j. Draw a line passing through points N and R.
k. The intersection of the two lines is point S.
l. Measure the distance from S to M using a ruler. This is the length /NM/.
m. Draw a line passing through points P and S.
n. Measure the angle between lines PR and PS using a protractor. This is angle PRQ.
Note that the construction should be done accurately to get the correct measurements.