The diagram represents 2 straight lines OA,OB inclined at an angle 2a. The circle of centre P1 has radius a and touches
Posted: Tue Jul 12, 2022 12:47 pm
- The Diagram Represents 2 Straight Lines Oa Ob Inclined At An Angle 2a The Circle Of Centre P1 Has Radius A And Touches 1 (60.09 KiB) Viewed 31 times
The diagram represents 2 straight lines OA,OB inclined at an angle 2a. The circle of centre P1 has radius a and touches each of OA and OB.A sequence of circles is drawn, decreasing in radius, each touching OA,OB and its immediate predecessor. Prove that the areas of the circles are in geometric progression. The sum of the first n of these circles is Sn and the sum to infinity of the geometric progression is S. Prove that the difference S−Sn is less than 1001S whenever n exceeds lg(1−sinα1+sinα)1. [Note :lgx=log10x ] Prove that the area of the first circle is equal to the sum of the areas of all the other circles when sinα=3−22.