Ex 5.1, 3

Transcript

Ex 5.1, 3 Draw △ABC, with AB=6" " cm,BC=7" " cm and CA=7" " cm. Draw the circumcircle of △ABC. Let the circumcentre be O . Measure OA, OB,OC. We follow these steps Draw side AB Make AC = 7 cm from point A, BC = 7 cm from point B Where they intersect is point C 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 6 cm 2. Since AC = 7 cm Open compass to 7 cm. Pointy end at A, make an arc 3. Since BC = 7 cm Open compass to 7 cm. Pointy end at B, make an arc 4. Where the two arcs intersect is point 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 We are asked to measure OA, OB and OC Thus, OA = OB = OC = 3.9 cm This circle is our circumcircle And, center O is our circumcenter, which lies inside the triangle