First slide

Cartesian plane

Question

$If (0, 0) is orthocentre of triangle formed by A (\cos α, \sin α), B (\cos β, \sin β) and C (\cos γ, \sin γ) then ∠ B A C is$

Moderate

A

$60 °$
B

$30 °$
C

$45 °$
D

$22 \frac{1 °}{2}$

Solution

$Points A (\cos α, \sin α), B (\cos β, \sin β), C (\cos γ, \sin γ) are$
equidistant from origin O(0, 0). $O A = \sqrt{\sin^{2} α + \cos^{2} α} = 1 s i m i l a r l y O B = 1, O C = 1$
Thus, circumcenter is origin.
Also orthocenter is origin. circumcenter and orthocenter are coincident, So triangle is equilateral
$∴ ∠ B A C = 60^{\circ}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App