Q. 23.5( 6 Votes )

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?

Answer :


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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