If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

Two chords AB and AC of the larger of two concentrci circles touch the other circle at points P and Q respectively. Prove that PQ = 1/2BC .

Two circles intersect each other at P externally. The straight QR touches the circle at two points Q and R. Prove that /_QPR = 1 right angle.

Q, R, S are the points on the line joining the point P(a,x) and T(b,y) such that PQ=QR=RS=ST, then ((5a+3b)/8, (5x+3y)/8) is the midpoint of the segment

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

In trianglePQR , M and N are two points on PQ and PR such MN || QR and PM = 1/2 QM. If QR = 4.5cm. Then MN =

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

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 .

PQ is a diameter of a circle and AB is such a chord of it that it is perpendicular to PQ . If C be the point of intersection of PQ and AB , then prove that PC.QC=AC.BC .

Draw a triangle PQR , such that PQ = 6cm, QR= 5cm, and PR = 6 cm.

ABC is a right-angled triangle of which /_A = right angle. P and Q are two points on AB and AC respectively.By joining P,Q,B,Q and C,P prove that BQ^(2) + PC^(2) = BC^(2) + PQ^(2)