Question
The centres of two circles C1 and each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1\displaystyle{\quad\text{and}\quad}{C}{2}{\quad\text{and}\quad}{C}{b}{e}{a}\circ\le\to{u}\chi{n}{g}\circ\le{s}{C}{1}{\quad\text{and}\quad}{C}{2}{e}{x}{t}{e}{r}{n}{a}{l}{l}{y}.{I}{f}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{1}{\quad\text{and}\quad}{C}{p}{a}{s}{\sin{{g}}}{t}{h}{r}{o}{u}{g}{h}{P}{i}{s}{a}{l}{s}{o}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{2}{\quad\text{and}\quad}{C},{t}{h}{e}{n}{t}{h}{e}{r}{a}{d}{i}{u}{s}{o}{f}{t}{h}{e}\circ\le{C}{i}{s}
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The tangent at point P on an ellipse intersects the major axis at T and N is the food of the perpendicular from P to the same axis. Show that the circle drawn on NT diameter interesects the auxiliary cicrle orthogonally. Question Text | The centres of two circles C1 and each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1\displaystyle{\quad\text{and}\quad}{C}{2}{\quad\text{and}\quad}{C}{b}{e}{a}\circ\le\to{u}\chi{n}{g}\circ\le{s}{C}{1}{\quad\text{and}\quad}{C}{2}{e}{x}{t}{e}{r}{n}{a}{l}{l}{y}.{I}{f}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{1}{\quad\text{and}\quad}{C}{p}{a}{s}{\sin{{g}}}{t}{h}{r}{o}{u}{g}{h}{P}{i}{s}{a}{l}{s}{o}{a}{c}{o}{m}{m}{o}{n}{\tan{\ge}}{n}{t}\to{C}{2}{\quad\text{and}\quad}{C},{t}{h}{e}{n}{t}{h}{e}{r}{a}{d}{i}{u}{s}{o}{f}{t}{h}{e}\circ\le{C}{i}{s} |