State True or False. In a circle with Centre $$O$$, $$AB$$, $$BC$$ are two chords each of length 3 units. If the area of the quadrilateral $$OABC$$ is 6 sq. units then the radius of the circle is 5 units.

$$OB$$ splits $$OABC$$ into two congruent triangles $$OAB$$ and $$OCB$$, each of area 3. In isosceles triangle $$OAB$$ with base 3, the height is $$\sqrt{r^2 - \frac{9}{4}}$$, so $$\frac{1}{2} \times 3 \times \sqrt{r^2 - \frac{9}{4}} = 3$$. This gives $$r^2 = 4 + \frac{9}{4} = \frac{25}{4}$$ and $$r = 2.5$$, not 5. The statement is False.