A triangle {ABC} with vertices {A} \equiv(2,5), {B} \equiv(5,2) and {C} \equiv(-1,-1) inscribed on the curve x y-x-y-3=0 and H \equiv(\alpha, \alpha) is orthocenter. Let D, E and F be the feet of perpendiculars from {A}, {B} and {C} on {BC}, {CA} and {AB} respectively and inradius of ∆ {DEF} is {r} then

Correct Answer is : r=25√2 units

Orthocenter of triangle {ABC} is (-1,-1)

Equation of {DE} is {x}+ {y}-\frac{13}{5}=0

JEE Advanced 2020 Full Test 1 Paper 2

Question : 40 of 54

Marks: +1, -0

A triangle ABC with vertices A≡(2,5),B≡(5,2) and C≡(−1,−1) inscribed on the curve xy−x−y−3=0 and H≡(α,α) is orthocenter. Let D,E and F be the feet of perpendiculars from A,B and C on BC,CA and AB respectively and inradius of ∆DEF is r then

Orthocenter of triangle ABC is (-1,-1)
Equation of DE is x+y−‌
13
5
=0
r=‌
4
5
√2 units
r=‌
2
5
√2 units

Validate

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