Consider-the-quadrilateral-ABCD-The-points-M-N-P-and-Q-are-the-midpoints-of-the-sides-AB-BC-CD-and-DA-Let-X-AP-BQ-Y-BQ-CM-Q-CM-DN-and-T-DN-AP-Prove-that-XYZT-AQX-BMY- Tinku Tara June 4, 2023 Geometry 0 Comments FacebookTweetPin Question Number 16946 by Tinkutara last updated on 28/Jun/17 ConsiderthequadrilateralABCD.ThepointsM,N,PandQarethemidpointsofthesidesAB,BC,CDandDA.LetX=AP∩BQ,Y=BQ∩CM,Q=CM∩DNandT=DN∩AP.Provethat[XYZT]=[AQX]+[BMY]+[CNZ]+[DPT]. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: A-distance-of-200-km-is-to-be-covered-by-car-in-less-than-10-hours-Yash-does-it-in-two-parts-He-first-drives-for-150-km-at-an-average-speed-of-36-km-hr-without-stopping-After-taking-rest-for-30-miNext Next post: Through-the-vertices-of-the-smaller-base-AB-of-the-trapezoid-ABCD-two-parallel-lines-are-drawn-intersecting-the-segment-CD-These-lines-and-the-trapezoid-s-diagonals-divide-it-into-seven-triangles-an Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.
![Consider the quadrilateral ABCD. The points M, N, P and Q are the midpoints of the sides AB, BC, CD and DA. Let X = AP ∩ BQ, Y = BQ ∩ CM, Q = CM ∩ DN and T= DN ∩ AP. Prove that [XYZT] = [AQX] + [BMY] + [CNZ] + [DPT].](https://www.tinkutara.com/question/Q16946.png)