Q. Area of the triangle formed by pair of tangents and the corresponding chord of contact?

Kamal Bahadur

Q. Area of the triangle formed by pair of tangents and the corresponding chord of contact for a circle is (R is the radius of circle and L is length of tangent)

a)

b)

c)

d)

Manasi

in the bigger triangle sin @ = R / (L²+ R²)^1/2 ....................(A)

cos @ = L / (L²+ R²)^1/2....................(B)

Now the area of the required triangle (the shaded area) = b X h

in smaller triangle, with angle @ .... h = L cos @ and b = L sin @

therefore, the area = L² sin @ cos @ substituting values from (A) and (B)

= RL³ / (L²+ R²)

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