Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

The radius of the circle passing through the centre of the inscribed circle of the $\Delta$le ABC and through the end point of the base BC is R then $\large\frac{a}{R}$$\sec \large\frac{A}{2}$ is equal to

$(a)\;3\qquad(b)\;4\qquad(c)\;2\qquad(d)\;0$

1 Answer

Comment
A)
Step 1:
Let $O$ be the centre of the inscribed circle of triangle ABC.We have drawn another circle passing through $O,B$ and $C$.Suppose radius is equal to $R$.
Applying sine rule in $\Delta OBC$,we get
$\large\frac{a}{\sin \angle BOC}$$=2R$
$\Rightarrow R=\large\frac{a}{2\sin \angle BOC}$-----(1)
Now,since $O$ is the centre of the inscribed circle,hence $BO$ and $CO$ are bisections of angles $B$ and $C$ respectively.
$\angle OBC=\large\frac{B}{2}$
$\angle OCB=\large\frac{C}{2}$
$\angle BOC=180^{\large\circ}-\big(\large\frac{B}{2}+\frac{C}{2}\big)$
$\qquad\;\;=180^{\large\circ}-\big(90^{\large\circ}-\large\frac{A}{2}\big)$
$\qquad\;\;=90^{\large\circ}+\large\frac{A}{2}$
Step 2:
Substituting the value in (1) we get,
$R=\large\frac{a}{2\sin (90^{\large\circ}+\large\frac{A}{2}\big)}$
$\;\;=\large\frac{a}{2}$$\sec\large\frac{A}{2}$
$\;\;=\large\frac{a}{R}$$\sec\large\frac{A}{2}$
$\;\;=2$
Hence (c) is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...