Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
1.3k views
in Combinations by (44.0k points)
closed by

There are 12 distinct points A, B, C, …, L, in order, on a circle. Lines are drawn passing through each pair of points.

(i) How many lines are there in total?

(ii) How many lines pass through D?

(iii) How many triangles are determined by lines?

(iv) How many triangles have on vertex C?

1 Answer

+1 vote
by (44.0k points)
selected by
 
Best answer

(i) We need two points to draw a line.

∴ Total number of lines = 12C2 = 66

(ii) Lines are drawn passing through each pair of points.

∴ Lines from point D will pass through all the remaining 11 points.

∴ 11 lines pass through D.

(iii) We need three points to draw a triangle.

∴ Number of triangles = 12C3 = 220

(iv) To get the triangles with one vertex as C, we need two vertices from the remaining 11 vertices

∴ Number of triangles with vertex at C = 11C2

\(\frac{11\times10}2\) = 55

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.

...