Draw a triangle ABC in which BC
B = 110° and AB = 4.5 cm. Draw its altitudes. Does the
orthocenter lie out side the triangle?
Answers
Answer:
Steps for construction:
I) Construction of triangle
1) Let the base of the triangle be BC=7cm.
2) With taking B as the centre, draw ∠ABC=60
o
with the help of a protractor and draw ray BX.
3) Measure 5cm on your compass and with B as the centre, mark point A at 5cm from B on ray BX.
4) Join points A and C to get △ABC.
II) Construction of perpendicular bisectors
1) Taking B as the centre and radius more than half of BC, mark arcs below and above the line.
2) Now, with A as the centre and same radius, draw arcs above and below the line to intersect the already drawn arcs. Name the new points as P and Q.
3) Join points P and Q. This line PQ is the required perpendicular bisector of side BC.
4) Similarly, draw perpendicular bisectors of sides AB and AC.
III) Construction of circumcircle
1) All the perpendicular bisectors of △ABC will intersect at one point in the interior of the triangle.
Name that point as O.
2) Taking point O as the centre and OA as the radius draw a circle. Points B and C should also lie on the circle.
3) This is the required circumcircle.
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