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

let P be a point on circumcircle of triangle ABC. perpendiculars PL,PM and PN are drawn on BC,CA and AB respectively. show that L,M,N are collinear

let P be a point on circumcircle of triangle ABC. perpendiculars PL,PM and PN are drawn on BC,CA and AB respectively. show that L,M,N are collinear

Grade:11

1 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Dear student

To Prove: N, M, and L are collinear.
Construction: Join PA and PC.Proof: ∠PMA +∠ANP = 90° + 90° = 180°Therefore, points A, M, P, N are concyclic....∠PMN =∠PAN ................... (i)
(angles in the same segment)Again ∠PMC =∠PLC = 90°Therefore, quadrilateral PMLC is cyclic....∠PML +∠PCL=180° ................... (ii)
Now, ∠PAB +∠PCB = 180°and ∠PAN +∠PAB = 180°...∠PAN =∠PCB =∠PCL ................... (iii)
From Equations (i) (ii) and (iii) we get,∠PML +∠PCL=∠PML +∠PAN=∠PML +∠PMN = 180°Hence, N, M, L are collinear. (NML line is called Simpson's line.

Regards

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