# Math

An isosceles triangle ABC has its vertices on a circle. If AB=13cm,BC =13cm and AC=10cm, calculate:the height BM of the triangle. Calculate the radius of the circle, to the nearest whole cm

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1. The height can be calculated using the Pythagorean Theorem : )
c^2 = a^2 + b^2

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2. Then the radius is half of the height : )

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3. BM divides the base into two 5cm sections, giving you two 5-12-13 right triangles. So, BM = 12.
Let the center of the circle be O. BM = OM + r = 12.
Now you have an isosceles triangle MOC whose sides are 12-r, r-5, and 5.
So, now just solve
5^2 + (12-r)^2 = r^2

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👨‍🏫
oobleck
4. ooooops! The triangle does not hit the outside edge of the circle, thus the height must be more than 5 : ) So sorry... I haven't had my first cup of tea yet.
Oobleck has an outstanding solution : )

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5. a. X = AC/2 = 10/2 = 5 cm.
Y = BM = height.
x^2 + y^2 = 13^2,
5^2 + y^2 = 169,
Y = 12 cm.

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