Question

Fig. 24
A
52
21. In the following Fig., A ABC is isosceles with AB = AC and
ZA = 52º. Bisectors of Z B and Z C meet at 0. Find :
(1) Z ABC
(ii) Z OBC
(iii) Z BOC
B
B Fig. 25​

Answer 1

Answer:

REF.image

To prove : AB×EF=AD×EC

⇒

EC

AB

=

EF

AD

Proof :

AB=AC (∵ ABC is isosceles)

∴∠B=∠C (angles opposite to equal sides are equal) - (1)

In ΔABD and ΔECF

∠ABD=∠ECF (from (1))

∠ADB=∠EFC (Both are 90

∘

)

Using AA similarity

ΔADB∼ΔECF

⇒

EC

AB

=

EF

AD

⇒AB×EF=AD×EC

∴ Hence proved.

solution

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