LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
8.3k views
in Circle by (49.7k points)
closed by

Theorem: If secants containing chords AB and CD of a circle intersect outside the circle in point E, then AE × EB = CE × ED.

1 Answer

+1 vote
by (49.1k points)
selected by
 
Best answer

Given: Chords AB and CD of a circle intersect outside the circle in point E. 

To prove: AE × EB = CE × ED 

Construction: Draw seg AD and seg BC.

Proof:

In ∆ADE and ∆CBE, ∠AED = ∠CEB [Common angle] ∠DAE ≅ ∠BCE [Angles inscribed in the same arc] 

∴ ∆ADE ~ ∆CBE [AA testof similaritv] 

∴ AE/CE = ED/EB [Corresponding sides of similar triangles] 

∴ AE × EB = CE × ED

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.

...