using ruler and compass only construct a triangle ABC having given 'c' =6cm , 'b' = 7cm and angle A =30° . Measure side 'a' . Draw the circumcircle of the triangle.
Answers
Given:
ΔABC having the length of side AC, c = 6cm, the length of side BC, b = 7cm, and ∠ BAC =30°.
To find:
The length of side AB, a, and the circumcircle of the triangle, ΔABC.
Solution:
ΔABC with AC = 6cm, BC = 7cm and ∠ BAC =30° can be constructed by the following steps.
Step 1: Draw the arm AC = 6cm
Step 2: Then place the point of the compass at A and draw an arc such that it passes through C.
Step 3: Now place the point of the compass at C and draw an arc such that it passes through A. The arc drawn at this step should cut the arc drawn in the above step at D.
Step 4: Now join A to B. The angle formed at A, ∠DAC = 60°.
Step 5: With the compass at C, draw another arc near a point B.
Step 6: Now with the point of the compass at D, draw another arc to cut the arc drawn in step 5 at B.
Step 7: Now join point B to point A. Now the ∠BAC is 30°.
Step 8: Now join BC to obtain ΔABC.
Now, measure the side AB to find the length of a.
A circumcircle of a triangle is a circle which circumscribes the triangle and touches each vertex of the triangle.
To construct the circumcircle of ΔABC, the following steps can be used.
Step 1: Draw the perpendicular bisectors of the sides AB, AC and BC and take their point of intersection as O.
Step 2: Taking point O as the centre, we draw a circle which touches each vertex of the triangle.
Step 3: The distance OA, OB and OC is said to be the circumradius and point O is said to be their circumcentre.
Hence, ΔABC having the length of side AC, c = 6cm, the length of side BC, b = 7cm, and ∠ BAC =30° is constructed and the required circumcircle of ΔABC is also constructed with the circumcentre O.
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