Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Q.

In the given figure, DEFG is a square and $∠$ BAC=90° State if the condition

${DE}^{2} = BD \times EC$ , is true or false.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

a

True

b

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that, DEFG is a square and ∠BAC=

90^{°} .

Question Image

We can write that,
In ΔAFG and ΔDB
∠GAF=∠BDG
∠AGF=∠DBG (corresponding angles because GF|| BC and AB are the transversal )
ΔAFG≈ΔDBG (by AA Similarity Criterion)
In ΔAGF&ΔEFC
∠AFG=∠CEF
∠AFG=∠ECF (corresponding angles because GF|| BC and AC is the transversal)
ΔAFG≈ΔEFC (by AA similarity criterion)
The ratio of the corresponding sides of similar triangles are equal.
Hence, we can write that,

\frac{BD}{EF} = \frac{DG}{EC}

\frac{BD}{DE} = \frac{DE}{EC}

{DE}^{2} = BD \times EC

Therefore, the given statement is true i.e.,

{DE}^{2} = BD \times EC

.
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Not sure what to do in the future? Don’t worry! We have a FREE career guidance session just for you!

In the given figure, DEFG is a square and ∠ BAC=90° State if the conditionDE2=BD×EC, is true or false.