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

In ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?


A

DC2×ED=EC2×AD

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

ED2×DC=EC2×AD

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

ED2×DC=AD2×EC

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

DC2×ED=AD2×EC

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

The correct option is B

ED2×DC=EC2×AD


In ABC and BDC

ABC=BDC=90

BCA=ECD (common in both the triangles)

Therefore, ABCBDC (by AA similarity criterion)

BCDC=ACBCBC2=AC×DC....(1)

Similarly, BDCDEC

Therefore, DCEC=BCDC
DC2=EC×BC

BC=DC2EC....(2)

On substituting (2) in (1), we get

DC4EC2 = AC×DC

DC3=EC2×AC

DC2×DC=EC2×(AD+DC)

(EC2+ED2)×DC=EC2(AD+DC)(DC2=EC2+ED2)

Therefore, ED2×DC=EC2×AD


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