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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