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
10.8k views
in Circle by (46.9k points)
closed by

i. Draw segment AB. Draw perpendicular bisector l of the segment AB. Take point P on the line l as centre, PA as radius and draw a circle. Observe that the circle passes through point B also. Find the reason.

ii. Taking any other point Q on the line l, if a circle is drawn with centre Q and radius QA, will it pass through B? Think. 

iii. How many such circles can be drawn, passing through A and B? Where will their centres lie?

1 Answer

+2 votes
by (47.6k points)
selected by
 
Best answer

i. Draw the circle with centre P and radius PA. 

line l is the perpendicular bisector of seg AB.

Every point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. 

∴ PA = PB … [Perpendicular bisector theorem] 

∴ PA = PB = radius 

∴ The circle with centre P and radius PA passes through point B.

ii. The circle with any other point Q and radius QA is drawn. 

QA = QB = radius … [Perpendicular bisector theorem]

∴ The circle with centre Q and radius QA passes through point B. 

iii. We can draw infinite number of circles passing through A and B.

All their centres will lie on the perpendicular bisector of AB (i.e., line l)

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.

...