Sarthaks Test
0 votes
4.9k views
in Mathematics by (7.9k points)

Below fig. shows a sector of a circle, centre O. containing an angle θ°. Prove that

(i) Perimeter of shaded region is r(tan θ+secθ+(πθ/180)−1)

(ii) Area of shaded region is (r2/2)(tanθπθ/180)

1 Answer

0 votes
by (13.1k points)
selected by
 
Best answer

Given angle subtended at centre of circle = θ

∠OAB = 90° [At joint of contact, tangent is perpendicular to radius]

OAB is right angle triangle

Perimeter of shaded region = AB + BC + (CA arc)

Area of shaded region = (area of triangle) – (area of sector)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...