the area of the triangle formed by the tangents from the points (h,k) to the circle x^2 +y^2=a^2 and the line joining the pint of contact is-----

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestthnks ,sir – Sumedh Bang · 3 years, 2 months ago

Log in to reply

If \(P\) is the point \((h,k)\), \(X,Y\) the points of tangency with the circle, and \(O\) the centre of the circle, then the kite \(OXPY\) has area \(a\sqrt{h^2+k^2-a^2}\), while the triangle \(OXY\) has area \(a^2\sin\theta\cos\theta\), where \(\theta = \angle XOP\). Since \[ \sin\theta \; = \; \frac{\sqrt{h^2+k^2-a^2}}{\sqrt{h^2+k^2}} \qquad \cos\theta \; = \; \frac{a}{\sqrt{h^2+k^2}} \] we deduce that the area of the triangle \(PXY\) is \[ \frac{a(h^2+k^2-a^2)^{\frac32}}{h^2+k^2} \] – Mark Hennings · 3 years, 2 months ago

Log in to reply