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प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
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उत्तर
Using distance formula, we have
AB = `sqrt((2-5)^2+(-2-2)^2)=sqrt(9+16)=5`
BC = `sqrt((-2-2)^2+(t+2)^2)=sqrt(t^2+4t+20)`
AC = `sqrt((-2-5)^2+(t-2)^2)=sqrt(t^2-4t+53) `
Now, it is given that △ABC is right angled at B.
Using the Pythagorean theorem, we have
AB2 + BC2 = AC2
∴25+t2+4t+20=t2−4t+53 [From (1), (2) and (3)]
⇒45+4t=−4t+53
⇒8t=8
⇒t=1
Hence, the value of t is 1.
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