badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

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
Menu
Grade:

                        

as shown in the figure AD is the altitude on BC and AD produced meets the circumcircle of traingle ABC at P where DP =x . similarly EQ=y and FR = z . if a, b ,c respectively denotes the sides BC, CA, and AB , then a/2x+b/2y+c/2z has the value equal to

2 years ago

Answers : (1)

Aarushi Ahlawat
41 Points
							
Use the intersection chord theorem to get relation between a/2x, b/2y and c/2z. NOw write a, b, and c as sum of two parts of the side e.g a=BD+DC and so on. Convert the ratios to trigonometric ratios of specific angle and you should get answer in the form of sum of trigonometric ratios of the angle angles. Further simplication is possible with the fact that A+B+C=pi.
 
for Two intersecting chords BC and AP
 
AD X x=BD X DC
 
\frac{a}{2x}=\frac{(BD+ DC)AD}{2BDXDC}
 
=\frac{1}{2}\left ( \frac{AD}{DC}+\frac{AD}{BD} \right )
=\frac{1}{2}\left ( tan(C)+tan(B) \right )
 
similarly 
 
\frac{b}{2y}=\frac{1}{2}\left ( tan(A)+tan(C) \right )
\frac{c}{2z}=\frac{1}{2}\left ( tan(A)+tan(B) \right )
 
Hence
 
\frac{a}{2x}+\frac{b}{2y}+\frac{c}{2z}=tan(A)+tan(B)+tan(C)
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


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

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


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details