Interesting Geometry Question

#Geometry #MathProblem #Math

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 7 years, 9 months ago

Thank you!

Sangeeta Mishra - 7 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.

Lakshaya Bangur - 7 years, 9 months ago

answer =90

Shubhabrota Chakraborty - 7 years, 9 months ago

use trigonometry. tangenta formula

Vali Dobre - 7 years, 9 months ago

This was in our fiitjee booklet last year.Quite easy

Priyatam Roy - 7 years, 9 months ago

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

Subhrodipto Basu Choudhury - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$