The circles having radii r1 and r2 intersect orthogonally. Length of their common chord is

Question

Arun Kumar · Answer

Two circles intersect orthogonally means r1 through point of contact makes right angle with r2 through that point

so the line intersecting has lenght

$\sqrt{r_{1}^2+r_{2}^2}$

common chord length = h

by equating area of triangle formed in 2 different way

$(1/2)r_{1}{r_{2}}=(1/2)(h/2)(\sqrt{r_{1}^2+r_{2}^2}) \\=>h=2*r_{1}{r_{2}}/(\sqrt{r_{1}^2+r_{2}^2})$

Arun Kumar

IIT Delhi

Askiitians Faculty

mayank rajput · Answer

you can solve this by using cosine formula in resulting triangl e if abc is a triangle then C*2=A*2+B*2-2ABcosm where m is angle between sides opposite to angle c.

Abhishek Mehta · Answer

you can solve this by using cosine formula in resulting triangleif abc is a triangle thenC*2=A*2+B*2-2ABcosmwhere m is angle between sides opposite to angle c.

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The circles having radii r1 and r2 intersect orthogonally. Length of their common chord is

The circles having radii r1 and r2 intersect orthogonally. Length of their common chord is

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The circles having radii r1 and r2 intersect orthogonally. Length of their common chord is

The circles having radii r1 and r2 intersect orthogonally. Length of their common chord is

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