The two points `P` and `Q` are on a straight line, At the points `P` and `Q`, `PR` and `QS` are perpendicular on the straight line. `PS` and `QR` intersect each other at the point `O`. `OT` is perpendicular on `PQ`. Prove that `(1)/(OT)=(1)/(PR)+(1)/(QS)`.

Find the perpendicular distance of the straight line 4x-y=5 from the point (2,-1)

In a right angled traingle PQR , angleP is right angle and PS is perpendicular to the hypetnuse QR. Prove that 1/(PS^2)-1/(PQ^2)=1/(PR^2)

If the straight line joining the points (4, -3, 2) and (3, -1, 5) is perpendicular to the straight line joining the points (m, -2, 1) and (7, 3, -2), then the value of m is -

Show that the staright line joining the points (-1, 0, -2) and (1, 3, -1) is perpendicular to the straight line joining the points (9, 1, -6) and (7, 2, -5)

The two circles with centre X and Y intersect each other at the points A and B, A joined with the mid -point S of XY and the perpendicular on SA through the point A is drawn which intersect the two circles at the point P and Q .Prove that PA = AQ.

The perpendicular distance of the straight line 6x-8y=25 from the point (-1,-4) is -

Two circles intersect each other at the points G and H . A straight line is drawn through the point G which intersect two circles at the points P and Q and the straight line through the point H parallel to PQ intersects the two circles at the points R and S . Prove that PQ=RS .

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

Mark two points P and Q. Draw a line through P and Q. Now how many lines are parallel to PQ, can you draw?

A straight line intersects one of the two concentric circles at the points A and B and other at the points C and D. Prove that AC = BD.