Let-ABCD-be-a-square-and-M-N-points-on-sides-AB-BC-respectably-such-that-MDN-45-If-R-is-the-midpoint-of-MN-show-that-RP-RQ-where-P-Q-are-the-points-of-intersection-of-AC-with-the-lines-MD-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 24684 by Tinkutara last updated on 24/Nov/17

Let ABCD be a square and M, N points on sides AB, BC respectably, such that ∠MDN = 45°. If R is the midpoint of MN show that RP = RQ where P, Q are the points of intersection of AC with the lines MD, ND.

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{square}\:\mathrm{and}\:{M},\:{N}\:\mathrm{points} \\ $$$$\mathrm{on}\:\mathrm{sides}\:{AB},\:{BC}\:\mathrm{respectably},\:\mathrm{such}\:\mathrm{that} \\ $$$$\angle{MDN}\:=\:\mathrm{45}°.\:\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of} \\ $$$${MN}\:\mathrm{show}\:\mathrm{that}\:{RP}\:=\:{RQ}\:\mathrm{where}\:{P},\:{Q} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{points}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:{AC}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{lines}\:{MD},\:{ND}. \\ $$

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Let-ABCD-be-a-square-and-M-N-points-on-sides-AB-BC-respectably-such-that-MDN-45-If-R-is-the-midpoint-of-MN-show-that-RP-RQ-where-P-Q-are-the-points-of-intersection-of-AC-with-the-lines-MD-

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