Dhaka regional 16 P4

For students of class 9-10 (age 14-16)
mdhasib
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Dhaka regional 16 P4

Unread post by mdhasib » Mon Jan 09, 2017 12:23 pm

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Thanic Nur Samin
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Re: Dhaka regional 16 P4

Unread post by Thanic Nur Samin » Fri Jan 13, 2017 1:22 am

Let the reflection of $X$ across $Y$ be $Z$. Now, see that $\angle PQX=\angle PRZ, \angle PQR=\angle PXY=\angle PZR$ and finally $PQ=PR$. These imply that $\triangle PQX\cong \triangle PRZ$. So $QX=RZ$, and thus $QX+RX=RZ+RX=XZ=2XY=24$
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Absur Khan Siam
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Re: Dhaka regional 16 P4

Unread post by Absur Khan Siam » Fri Jan 13, 2017 6:13 pm

How can you write $XZ = 2XY$?
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

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ahmedittihad
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Re: Dhaka regional 16 P4

Unread post by ahmedittihad » Fri Jan 13, 2017 6:31 pm

As $Z$ is defined as the reflected point of $X$ with right to $Y$, we get $ XY=YZ$. From there we get $XZ=2XY$.
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Absur Khan Siam
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Re: Dhaka regional 16 P4

Unread post by Absur Khan Siam » Fri Jan 13, 2017 7:10 pm

Sorry!I missed some questions. How ${\angle}PQX = {\angle}PRZ$ and${\angle}PQR = {\angle}PXY$?
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

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Thanic Nur Samin
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Re: Dhaka regional 16 P4

Unread post by Thanic Nur Samin » Sat Jan 14, 2017 12:06 pm

Absur Khan Siam wrote:Sorry!I missed some questions. How ${\angle}PQX = {\angle}PRZ$ and${\angle}PQR = {\angle}PXY$?
Learn the properties of cyclic quads. More than $50\%$ of all olympiad geometry problems exploit the usage of cyclic quad. https://www.expii.com/t/when-is-a-quadr ... on&id=1795
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

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