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Interesting Geometry Question

Note by Sangeeta Mishra
4 years, 1 month ago

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Construct point I, which is the reflection of D about FE.

\(\alpha = \angle IHE\)

\(\alpha+\beta = \angle IHE + \angle EHC = \angle CHI\)

Connect CI. Note that \(\triangle HCI\) is a right angled isosceles triangle, thus \(\angle CHI = 45^\circ \)

\(\gamma = 45^\circ\)

Thus sum of 3 angles \(=90^\circ\)

Clarence Chew - 4 years, 1 month ago

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Thank you!

Sangeeta Mishra - 4 years, 1 month ago

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answer =90

Shubhabrota Chakraborty - 4 years, 1 month ago

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y=45degree. alpha+ beta= 45 degree as tan ( a + b)= tan a + tan b /(1-tan a * tanb)= (1/2+1/3)/(1-1/2*1/3)=1 =90 degree.

Lakshaya Bangur - 4 years, 1 month ago

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90 degree!! tan^-1(1)+tan^-1(0.5)+tan^-1(1/3)=90

Subhrodipto Basu Choudhury - 4 years, 1 month ago

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This was in our fiitjee booklet last year.Quite easy

Priyatam Roy - 4 years, 1 month ago

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  1. use trigonometry. tangenta formula

Vali Dobre - 4 years, 1 month ago

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