Question

Triangle ABC with AB=AC=10cm and BC=12cm has been inscribed in
circle. Find the radius of the circle.........guys pls solve it.... urgent​

Answer 1

Step-by-step explanation:

here is your answer mate hope it helps you

Answer 2

The radius of the circle is 6.25 cm.

Step-by-step explanation:

It is given,

ABC is an isosceles triangle inscribed in a circle.

AB = AC = 10 cm

BC = 12 cm

let's draw AD as the median of the isosceles ∆ ABC such that AD perpendicular to BC.

The median drawn to an isosceles triangle is the perpendicular bisector of the base as well as the angle bisector of the angle opposite to the base.

BD = DC = $\frac{1}{2}BC= \frac{1}{2}\times 12 = 6 cm$

consider the right-angled ∆ ABD and by applying Pythagoras theorem, we get

AD ²= AB²-BD²

AD ²= (10)²- (6)²

AD ²= 100-36

AD ²= 64

AD=√64

AD= 8 cm

Let the radius of the circle with centre O be “r” cm.

OA = OB = OC = r cm

Since AD = 8 cm ∴ OD = [8 – r] cm

now, OB² = OD² + BD²

r² = [8 - r]² + 6²

r²= 64 +r²-16r +36

100-16r = 0

100= 16r

r = 6.25 cm

hence ,

the radius of the circle is 6.25 cm.

#Learn more:

An isosceles triangle ABC is inscribed in a circk. If AB - AC - 13 cm and BC = 10cm, find the  radius of the circle

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