Prove that equal

Given: AB = CD

Construction: Drop perpendiculars OX and OY on to AB and CD respectively and join OA and OD.

Here, OX AB (perpendicular from center to chord divides it into two equal halves)

AX = BX = – – (1)

OY CD (perpendicular from center to chords divides it into equal halves

CY = DY = – – (2)

Now, given that

AB = CD

=

AX = DY (from –1 and –2 ) – – (3)

In ΔAOX and ΔDOY

OXA = OYD (right angle)

AX = DY (from –3 )

BY RHS congruency

ΔAOXΔDOY

OX = OY (by C.P.C.T)

Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Arc of Circle And Related IMP Qs40 mins
IMP Qs Related with Circles For Boards44 mins
Chords Of Circles42 mins
IMP Theorems And Their Application43 mins
Circles- All kinds of Questions36 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

PQ and RQ are theRS Aggarwal & V Aggarwal - Mathematics

In a circle of raRD Sharma - Mathematics

Two equal circlesRD Sharma - Mathematics

Angle formed in mRD Sharma - Mathematics

If AB is aRD Sharma - Mathematics

The greatest chorRD Sharma - Mathematics

If two diameters RD Sharma - Mathematics

<span lang="EN-USRS Aggarwal & V Aggarwal - Mathematics