Question

circume enter of an isosceles triangle is O angle ABC = 120°, radius of circle is 5cm, lenght of ab​

Answer 1

Step-by-step explanation:

We have an isosceles ∆ABC, with vertex A, B, C lying on a circumcircle. Let O be centre of this circle. We have to find m(angle BAC)

We have AB=AC=AO, since AO is radius.

We also know segment AO lies on perpendicular bisector line of BC.

Denote intersection point of AO and BC as ‘M'. M is hence midpoint of BC.

It thus follows that ∆AMB and ∆AMC are congruent right angled triangles.

Note that B is equidistant from A & O, as well as C, making them lie on perpendicular bisector of AO, thus making M midpoint of AO as well.

Finally, it is obvious that AM = AO/2 = AB/2.

Thus, the triangles BAM and CAM are 30°-60°-90° triangles, where angle opposite to the side AM, i.e. angle ABM is of 30°.

It follows that angle BAM and angle CAM are 60° each; thereby making angle BAC = 120°.

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