In a triangle ABC, C is the supplement of an acute triangle. BC= 10cm, AC= 12cm. Find the total number of possible values of AB
using inequality
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Answer:
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Step-by-step explanation:
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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 = 1/2 BC = 1/2 × 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.
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