שני משולשים במרובע ומעגל – מדרגה 3 – Stepped Tasks

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שני משולשים במרובע ומעגל

מדרגה 3

נתון: $ABCD$ טרפז $(AD∥BC)$ .
$DC$ , $AD$ ו- $BC$ משיקים למעגל שמרכזו $O$ בנקודות $B$ , $E$ , $A$ .

$X$ – נקודת חיתוך של $BE$ ו- $OC$ .

$Y$ – נקודת חיתוך $AE$ ו- $OD$ .

הוכיחו: $OYEX$ מלבן (מצאו לפחות 3 דרכים שונות).

היעזרו ביישומון.

נתון: גם: $R$ – נקודת חיתוך של $OC$ עם המעגל.

המרובע $AERO$ הוא טרפז $(AE∥OR)$ .

$F$ – נקודת חיתוך $OE$ ו- $AR$ .

הוכיחו: שטח משולש $\triangle{AFO}$ שווה לשטח משולש $\triangle{EFR}$ .

תוכלו להיעזר ביישומון.

אחרי שפתרתם את הבעיות במדרגה 3, פתרו את בעיית המטרה.

יישומון לבעיה א

גרירת נקודות $A$ או $E$ , מציגה מרובע ומשולשים שונים, תוך שמירה על הנתונים.
כדי ל"נקות" את היישומון ולהתחיל מחדש ניתן להיעזר בחיצי האתחול שבפינה הימנית העליונה.

יישומון לבעיה ב

גרירת נקודות $A$ או $E$ , מציגה מרובע ומשולשים שונים, תוך שמירה על הנתונים.
כדי ל"נקות" את היישומון ולהתחיל מחדש ניתן להיעזר בחיצי האתחול שבפינה הימנית העליונה.

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