World's only instant tutoring platform
dropdown-logo
Become a tutorPartnershipsAbout usStudent loginTutor login
About us
Login
App StorePlay Store
Get 2 FREE Instant-Explanations on Filo with code FILOAPP
Two equal circles intersect in P and Q. A straight line throug
Question

Two equal circles intersect in and . A straight line through meets the circles in and . prove that

Views

Views: 742 students

tutor 0tutor 1tutor 2
Found 5 tutors discussing this question
Samuel Discussed
Two equal circles intersect in and . A straight line through meets the circles in and . prove that
6 mins ago
Discuss this question LIVE
6 mins ago

Text SolutionText solutionverified iconVerified

We know that two circles will congruent if they have equal radii

From the figure, we know that if two  chords are equal then the corresponding arcs are congruent

We know that is the common chord in both the circles

So their corresponding arcs are equal

It can be written as

Arc arc

We know that the congruent arcs have the same degree

So we get


We know that the base angles of an isosceles triangle are equal

So we get


Therefore, it is proved that
Was this solution helpful?
150
Share
Report
One destination for complete JEE/NEET preparation
One destination to cover all your homework and assignment needs
Learn Practice Revision Succeed
Instant 1:1 help, 24x7
Instant 1:1 help, 24x7
60, 000+ Expert tutors
60, 000+ Expert tutors
Textbook solutions
Textbook solutions
Big idea maths, McGraw-Hill Education etc
Big idea maths, McGraw-Hill Education etc
Essay review
Essay review
Get expert feedback on your essay
Get expert feedback on your essay
Schedule classes
Schedule classes
High dosage tutoring from Dedicated 3 experts
High dosage tutoring from Dedicated 3 experts
Trusted by 4 million+ students

Practice questions from similar books

Question 1
 The centres of two circles C1 and each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1\displaystyle{\quad\text{and}\quad}{C}{2}{\quad\text{and}\quad}{C}{b}{e}{a}\circ\le\to{u}\chi{n}{g}\circ\le{s}{C}{1}{\quad\text{and}\quad}{C}{2}{e}{x}{t}{e}{r}{n}{a}{l}{l}{y}.{I}{f}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{1}{\quad\text{and}\quad}{C}{p}{a}{s}{\sin{{g}}}{t}{h}{r}{o}{u}{g}{h}{P}{i}{s}{a}{l}{s}{o}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{2}{\quad\text{and}\quad}{C},{t}{h}{e}{n}{t}{h}{e}{r}{a}{d}{i}{u}{s}{o}{f}{t}{h}{e}\circ\le{C}{i}{s}

View solution

Question 2
Let P be the point on parabola which is at the shortest distance from the center S of the circle let Q be the point on the circle dividing the line segment SP internally. Then

View solution

Question 3
The points and are (a) vertices of an equilateral triangle (b) vertices of an isosceles triangle (c) vertices of a right-angled triangle (d) collinear

View solution

Question 4
Convert into a polar equation.

View solution

filo Logo
Doubt Icon Doubt Icon

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes
Question Text
Two equal circles intersect in and . A straight line through meets the circles in and . prove that
Answer TypeText solution:1
Upvotes150