On a circle of radius (r) ,3 points are chosen so that the circle is divided into 3 arcs in the ratio of 3:4:5. Tangents are drawn at the point of division. Find the area of triangle formed by the tangents.

Assuming O is the center of the circle.Arc(ACB)=3*arc(AB). Now as arc(ACB)+arc(AB)=3*arc(AB)+arc(AB)=circumference then arc(AB)=circumference/4 --> angle AOB=360/4=90 degrees. So, triangle AOB is a right isosceles triangle with OA=OB=r=3 --> hypotenuse AB=32+32−−−−−−√=32√AB=32+32=32 (or you can find the length of AB by applying the property of 45-45-90 right triangle where the sides are in the ratio 1:1:2√1:1:2).