 Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

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
`        Question number 10 prove that........................................`
3 months ago

```							there is a slight mistake in ques, but anyways we can correct it.we see that a ray y= tan(q) will intersect the circle x^2+y^2= a^2 at (acosq, asinq) which can be obtained by solving the two eqns together. so, A(acosq1, asinq1); B(acosq2, asinq2); C(acosq3, asinq3) now, we know that the circumcentre of ABC is obviously origin (0, 0). its centroid is [a(cosq1 + cosq2 + cosq3)/3, a(sinq1 + sinq2 + sinq3)/3].now, we use the fact that eulers line passes through orthocentre, centroid and circumcentre dividing them in ratio 2:1.let coordinates of orthocentre be (c, d). then by section formulaa(cosq1 + cosq2 + cosq3)/3 = (2*0+1*c)/(2+1)= c/3or a(cosq1 + cosq2 + cosq3)= c......(1)similarly, a(sinq1 + sinq2 + sinq3)/3= (2*0+1*d)/(2+1)= d/3or a(sinq1 + sinq2 + sinq3)= d.......(2)it is pretty obvious to see that (c, d) always lies on the line y/x = (sinq1 + sinq2 + sinq3)/(cosq1 + cosq2 + cosq3)or y= (∑sinqi)x/∑cosqikindly approve :=)
```
3 months ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Analytical Geometry

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 53 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions