# Interesting Geometry Question

Note by Sangeeta Mishra
4 years, 9 months 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 $$=90^\circ$$

- 4 years, 9 months ago

Thank you!

- 4 years, 9 months ago

- 4 years, 9 months ago

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.

- 4 years, 9 months ago

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

- 4 years, 9 months ago

This was in our fiitjee booklet last year.Quite easy

- 4 years, 9 months ago

1. use trigonometry. tangenta formula

- 4 years, 9 months ago