wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet in X and Y as shown. Join XY

These are the two statements:
Statement 1: AB is the perpendicular bisector of XY
Statement 2: XY is the perpendicular bisector of AB
Choose the correct option from below.


A

Both the statements are true

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

Only Statement 1 is true

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

Only Statement 2 is true

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

None of the statements are true

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

Both the statements are true


From the given question we can say that XY is the perpendicular bisector of AB. So, AOX = AOY = 90 and AO = OB. So, statement 2 is true.

If AB is a perpendicular bisector of line XY, it should divide XY in such a way that XO = OY and XOA = AOY = 90.

AOX=YOA

XOA=90 similarly YOA=90---------(1)

Join AX, AY and BX, BY.
Consider AOX and AOY,

AX = AY (same radius)

AO = AO (common side)
AOX AOY (By S.S.S congruency)
Hence OX = OY-----------(2)
From (1) and (2) we can say that AB is perpendicular bisector of XY.

So statement 1 is also true.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Perpendicular Bisector
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon