Ex 5.1, 2

Transcript

Ex 5.1, 2 Draw △ABC with AB=5" " cm,∠" " A=100^∘,AC=4" " cm. Draw the circumcircle of △ABC. Is the centre inside or outside the triangle? We follow these steps Draw side AB Make ∠" " 𝐀=〖𝟏𝟎𝟎〗^∘ In this ray, we mark point C such that AC = 4 cm To make circumcircle, we construct perpendicular bisectors of two sides Where the bisectors meet is center of circle, let’s mark it as O Make a circle, taking center as O, radius as OA (or OB, OC since OA = OB = OC) Let’s do it step by step Steps of construction – For making Triangle 1. Draw a line segment AB of length 5 cm 2. Draw ∠ A = 100° 3. Open the compass to 4 cm. Place the needle at A and draw an arc cutting the ray. Where the arc intersects the ray is point C 4. Join point B & C Thus, we made ∆ ABC 5. Now, we draw perpendicular bisector of AB Taking point A as center, radius more than ½ AB, we draw an arc on top and bottom of AB 6. Taking point B as center, radius same as previous, we draw an arc on top and bottom of AB 7. Join points where the two arcs intersect This is perpendicular bisector of AB 8. Now, making perpendicular bisector of AC Taking point A as center, radius more than ½ AC, we draw an arc on top and bottom of AC 9. Taking point C as center, radius same as previous, we draw an arc on top and bottom of AC 10. Join points where the two arcs intersect This is perpendicular bisector of AC 11. The point where both perpendicular bisectors meet is the Circumcenter Let’s mark it as O 12. Taking center as O, radius as OA – we draw a circle This circle is our circumcircle And, center O is our circumcenter, which lies outside the triangle