Question

One angle of a triangle is 110° and the side opposite to it is 4 centimetres long. What is its circumradius?

Answer 1

Let the given triangle be ABC with ∠ABC = 110° and AC = 4 cm.

We need to find the circumradius for this triangle, so we make ΔABC in such a way that points A, B and C lie on the circle.

Construction: Mark a point D such that line segment CD passes through the centre O of the circle.

Join points A and D.

As line segment CD passes through the centre of the circle, CD is the diametre.

We know that angle in a semicircle is a right angle.

∴ ∠DAC = 90°

Now, ABCD is a cyclic quadrilateral and the sum of opposite angles of a cyclic quadrilateral is 180°.

∴ ∠ADC + ∠ABC = 180°

⇒ ∠ADC + 110° = 180°

⇒ ∠ADC = 180° − 110° = 70°

In ΔDAC:

⇒ … (1)

We know that Sin 70° ≈ 0.9397 (From table)

Putting the value in (1):