an isoceles right triangle is inscribed in a circle. find the radius of the circle if one leg of the triangle is 8 cm
Answers
Answer:
Step-by-step explanation:
On the diagram, the two a's are the equal sides of the isosceles triangle and b is the distance from the center of the hypotenuse, h
, to the corner.
The distance b
can be calculated as
b=r+√r^2+r^2=(1+√2)r
.
By symmetry, we know that 12h=b,
so h=2b
.
We have
a=b^2+b^2−−−−−−√=2–√b
.
The perimeter can now be computed.
p=h+2a=2b+2(2–√b)=2(1+–√2)b=(6+4–√2)r
Since r=8
,
p=(6+4–√2)8=48+32–√2≈93.2548.
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Answer:
4√3 cm will be my answer.
Sol: Construct the figure.
We have a triangle ABC which is right angled at B and has a hypotenuse AC. The centre of the circle lies on the hypotenuse. Label the centre as O.
Now, from B, construct a median to AC. You will see, that the median connects at O.
Now, we have two triangles. Consider triangle OBC.
Angle BOC = 90° (Because OB is a median)
Hence triangle OBC is a right triangle.
Thus, BC² = OB² + OC²
=> 8² = OB² + 4² (OC = 4 because a median connects into the mid point of the opposite side.)
64-16 = OB²
48 = OB²
√48 = OB
√2×2×2×2×3 = OB
=> OB = 4√3 cm.