# Using the sine and cosine tables, and if needed a calculator, do these problems.A circle is to be drawn, passing through the ends of a line, 5 centimetres long; and the angle on the circle on one side of the line should be 80°. What should be the radius of the circle?

Let AB = 5 cm and BAC = 80°.

Now Let O be a midpoint of AB.

With O as centre and radius OA = OB,

Construct a circumcircle for Δ ABC.

We know that,

In circle, The angle formed by the diameter on its circumference

is always equal to 90° .

ABC = 90° ( AC is a diameter of circle O)

AC = AO + OC = r + r = 2r

In Δ ABC,

AB = AC × cos 80°

(From table, cos 80° = 0.173)

AC = 2r

r = 14.45 cm

Radius of a circle is 14.45 cm

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