Question Number 213745 by efronzo1 last updated on 15/Nov/24 Answered by mnjuly1970 last updated on 16/Nov/24 $$\:\left(\mathrm{M}{edian}\:{theorem}\:\right):\:\:\:\:\:\:\mathrm{7}^{\mathrm{2}} \:+\:{R}^{\mathrm{2}} =\:\mathrm{2}\left(\sqrt{\mathrm{14}}\:\right)^{\mathrm{2}} \:+\:\frac{\left(\mathrm{2}{R}\right)^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\mathrm{49}\:+\:{R}^{\mathrm{2}} \:=\:\mathrm{28}\:+\:\mathrm{2}{R}^{\mathrm{2}} \\…
Question Number 213203 by golsendro last updated on 01/Nov/24 $$\:\:\:\:\:\:\cancel{\underline{\underbrace{\mathscr{G}}}} \\ $$ Answered by lepuissantcedricjunior last updated on 01/Nov/24 $$\boldsymbol{{f}}\left(\boldsymbol{{xy}}\right)=\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{f}}\left(\boldsymbol{{y}}\right) \\ $$$$\boldsymbol{{f}}\left(\mathrm{10}\right)=\mathrm{14};\boldsymbol{{f}}\left(\mathrm{20}\right)=\mathrm{40} \\ $$$$\boldsymbol{{calculons}}\:\boldsymbol{{f}}\left(\mathrm{500}\right) \\…
Question Number 212993 by MrGaster last updated on 28/Oct/24 Commented by MrGaster last updated on 28/Oct/24 "Let ΔABC be inscribed in circle O. Point P is inside ΔABC, and the projections of P on the sides BC, CA, and AB are points X, Y, and Z, respectively. The second intersection point of line AP with circle O is D. Point E lies on circle O, and DE is perpendicular to BC. Let I be the midpoint of DE. Line PI intersects BC at F, and point T lies on AF such that TX is parallel to AD. Prove that line YZ bisects line TX." Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212986 by MrGaster last updated on 27/Oct/24 Commented by MrGaster last updated on 27/Oct/24 A, B are two fixed points on the same side of the line PQ. M is a moving point on PQ. When (|AM|+|BM|) is minimized, prove: angle AMP = angle BMQ Answered by mr W last updated on 29/Oct/24…
Question Number 212714 by Mingma last updated on 21/Oct/24 Answered by mr W last updated on 22/Oct/24 Commented by mr W last updated on 22/Oct/24…
Question Number 212647 by golsendro last updated on 20/Oct/24 $$\:\:\:\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}}\:+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}}\:=\:\mathrm{x}\: \\ $$ Commented by Rasheed.Sindhi last updated on 21/Oct/24 $${See}\:{also}\:{Q}#\mathrm{200498} \\ $$ Answered by Frix…
Question Number 212630 by efronzo1 last updated on 19/Oct/24 Commented by efronzo1 last updated on 19/Oct/24 $$\:\: \\ $$ Answered by mr W last updated…
Question Number 212377 by yadavd last updated on 12/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 211953 by efronzo1 last updated on 25/Sep/24 Commented by BHOOPENDRA last updated on 25/Sep/24 $${h}=\frac{\sqrt{\mathrm{2}}\:\left(\sqrt{{ab}}\:−{a}\:+{b}−{c}\right)}{\:\sqrt{\left(\sqrt{{ab}}\right)+{b}}} \\ $$ Commented by BHOOPENDRA last updated on…
Question Number 211495 by BaliramKumar last updated on 11/Sep/24 Answered by Rasheed.Sindhi last updated on 11/Sep/24 $${Let}\:{n}=\mathrm{10}{m} \\ $$$${HCF}\left(\mathrm{10}{m},\mathrm{10}\left({m}+\mathrm{1}\right)\right)=\mathrm{10} \\ $$$${HCF}\left({m},{m}+\mathrm{1}\right)=\mathrm{1}\Rightarrow{m}=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},… \\ $$$$\therefore{LCM}={x}\left(\mathrm{2}-{digit}\:{numbers}\right)=\mathrm{10}{m}\left({m}+\mathrm{1}\right)\: \\ $$$$\:\:\:\:\:\:=\mathrm{20},\mathrm{60}\:\left(\mathrm{2}\:{possible}\:{values}\right)…