Question

draw a circumcircle of a triangle with sides 6,8and 10 respectively. why does its circumcircle lies on a side of length 10 cm​

Answer 1

Question :-- Draw a circumcircle of a triangle with sides 6,8 and 10 respectively. why does its circumcircle lies on a side of length 10 cm..

Answer :--

❁❁ Refer To Image First .. ❁❁

Steps of construction :--

Step 1 :- Draw AB=8cm.

Step 2 :- Draw AC perpendicular to AB = 6 cm.

Than , by Pythagoras theoram , we have ,

→ BC = √(6)² + (8)² = √(36+64) = √100 = 10cm.

Step 3 :- Construct a bisector of all three sides, they will meet at a common point.

Step 4 :- Draw the circle with radius as the intersection point of the bisectors that pass through one of the vertex.

Now, Since the center of the circumscribed circle lies on the hypotenuse, the hypotenuse becomes the diameter of the circle.

Hence, we can say that, Radius of circum-circle of Right Angle ∆ = (Hypotenuse /2.)

Since the radii of the circle are congruent, a circumcenter is equidistant from vertices of the triangle. In a right triangle, the perpendicular bisectors intersect ON the hypotenuse of the triangle.