Check sibling questions

Example 5 - If arcs of same lengths in two circles subtend

Example 5 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Example 5 - Chapter 3 Class 11 Trigonometric Functions - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 5 If the arcs of the same lengths in two circles subtend angles 65ยฐ and 110ยฐ at the center, find the ratio of their radii. We know that ๐‘™ = r ฮธ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle ๐‘™ = r1 ฮธ = r1 ร— 65ยฐ = r1 ร— 65ยฐ ร— ๐œ‹/(180ยฐ) = r1 ร— 13๐œ‹/36 Length of arc of 2nd circle ๐‘™ = r2 ฮธ = r2 ร— 110ยฐ = r2 ร— 110ยฐ ร— ๐œ‹/(180ยฐ) = r2 ร— 11๐œ‹/18 Given that Length of I arc = length of II arc r1 ร— 13๐œ‹/36 = r2 ร— 11๐œ‹/18 ๐‘Ÿ1/๐‘Ÿ2 = 11๐œ‹/18 ร— 36/13๐œ‹ ๐‘Ÿ1/๐‘Ÿ2 = 22๐œ‹/13๐œ‹ ๐‘Ÿ1/๐‘Ÿ2 = 22/13 Hence r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.