Q1 of 9 Page 126

Construct ΔPQR with PQ = 5cm, ∠P = 100° and PR = 5cm and draw its circumcircle.

Rough Diagram:



Construction Steps:


Step 1: Draw the ΔABC with the given measurements.


geogebra-export.png


Step 2:


We know that the circum centre for an obtuse angled triangle lies outside the triangle.


Construct the perpendicular bisector of any two sides (PR and QR) and let them meet at S which is circum centre.



Step 3: With S as centre and SP = SQ = SR as radius draw the circum circle to pass through P, Q and R.



∴ The required circum circle for the given triangle is drawn above.


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Draw ΔABC with sides AB = 8 cm, BC = 7 cm and AC = 5 cm and construct its orthocentre.