If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

Class 9 Exam > Class 9 Questions > If two equal chords of a circle intersect wit...

Join the Discussion on the App

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord?

Join for Free

Join for Free

Verified Answer

If two equal chords of a circle intersect within the circle, prove tha...

Given AB and CD are chords of a circle with centre O. AB and CD intersect at P and AB = CD.

To prove : AP = PD and PB = CP.

Construction: Draw OM perpendicular to AB and ON perpendicular CD. Join OP.

AM = MB = 1/2AB (Perpendicular bisecting the chord)

CN = ND = 1/2CD (Perpendicular bisecting the chord)

AM = ND and MB = CN (As AB = CD)

In triangle OMP and ONP, we have,

OM = MN (Equal chords are equidistant from the centre)

<OMP = <ONP (90⁰)

OP is common. Thus triangle OMP and ONP are congruent (RHS).

MP = PN (cpct)

So, AM + MP = ND + PN

or, AP = PD (i)

As MB = CN and MP = PN,

MB - MP = CN - PN

= PB = CP (ii)

This question is part of UPSC exam. View all Class 9 courses

View all answers Start learning for free

Explore Courses for Class 9 exam

Similar Class 9 Doubts

If two equal chords of a circle intersects within the circle,prove that the segments of one chord are equal to corresponding chords of the other chords?

View answer

If two equal chords of a circle intersect within the circle prove that the line joining the point of intersection to the center makes equal angles withe the chord. Related: Angles Related to a Circle - Mathematics, Class 9

View answer

if two equal chords AB and CD intersect within the circle. prove that AD=BC

View answer

Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : If A and B are any two points on a circle, then the line segment AB is called a chord of the circle.Reason : Equal chords of a circle subtend equal angles at the centre.

View answer

Rohan draws a circle of radius 10 cm with the help of compass and scale. He also draws two chords, AB and CD in such a way that AB and CD are 6 cm and 8 cm from the centre O. Now, he has some doubts that are given below. Help him out by answering these questions:Q. Which statement is not true?

View answer

Top Courses for Class 9View all

Top Courses for Class 9

View all

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord?

Share with a Friend

Answer this doubt

Question Description
If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord?.

Solutions for If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? in English & in Hindi are available as part of our courses for Class 9. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.

Here you can find the meaning of If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? defined & explained in the simplest way possible. Besides giving the explanation of If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord?, a detailed solution for If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? has been provided alongside types of If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? theory, EduRev gives you an ample number of questions to practice If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord? tests, examples and also practice Class 9 tests.

Explore Courses for Class 9 exam