Construct Δ PQR such that ∠P = 70° , ∠R = 50° , QR = 7.3 cm and constructs its circumcircle.
By angle sum property of triangles,
In Δ PQR,
∠P + ∠Q +∠R = 180°
⇒ 70° + ∠Q + 50° = 180°
⇒ ∠Q = 60°
Steps of construction:
1. Draw a line QR = 7.3 cm.
2. With Q as centre, draw an angle of 60° using the protractor. Similarly, draw an angle of 50° with R as centre.
Where the rays RY and XQ meet, name the point as P.
Thus, Δ PQR is obtained.
3. Draw the perpendicular bisectors of the lines PR and QR. Let these perpendicular bisectors meet at point O.
4. With O as centre and OP as radius, construct a circle touching all the vertices of the Δ PQR.
This circle is thus the required circumcircle.