Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

In any ∆ABC,if I is the centre of the inscribed Circle, and if AI is produced to meet the circumscribed Circle at O; show that O is the centre of the Circle circumscribed about the triangle BIC.

In any ∆ABC,if I is the centre of the inscribed Circle, and if AI is produced to meet the circumscribed Circle at O; show that O is the centre of the Circle circumscribed about the triangle BIC.

Grade:12th pass

1 Answers

Aditya Gupta
2075 Points
one year ago
note that angle AOC= angleIOC= angle B (angles on the same chord)
we know that incenter is the point of intersection of angle bisectors of a triangle.
now, angle OIC= angle IAC + angle ICA= A/2 + C/2.
so, angle OCI= 180 – angle IOC – angle OIC= 180 – B – (A/2 + C/2)
= A+C – (A/2 + C/2)= A/2 + C/2
hence angle OCI= angle OIC
so that OI= OC
similarly OI= OB
since OI= OB= OC= R (say), O is the centre of the Circle circumscribed about the triangle BIC.
kindly approve :)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free