In `DeltaPQR`, `/_Q=2/_R`, The bisector of `/_PQR` intersects `PR` at the point `D`. Prove that `PQ*QR=QD.PR`.

In an isosceles right-angled triangle ABC, /_B=90^(@) . The bisector of /_BAC intersects the side BC at the point D. Prove that CD^(2) =2BD^(2)

In DeltaPQR , a straight line parallel to QR intersects PQ and PR at the points D and E respectively. If PD=2.4cm , PE=3.2cm and ER=4. 8cm , then the length of PQ is

In DeltaPQR , PQ=24cm , PR=32cm and PS is the bisector of /_QPR , where QS=8cm . Then the length of SR=

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 .

In the DeltaPQR , a straight line parallel to QR intersects the sides PQ and PR at the points L and M . If PL=n . PL and LQ=(p+1)LQ , then n-p=

PR is a diameter of a circle. A tangent is draewn at the point P and a point S is taken on the tangent of the circle is such a way that PR=PS. If RS intersects the circle at the point T., prove that ST =PT.

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

In DeltaPQR the straight line parallel to QR intersects the sides PQ and PR at the points E and F respectively. If EQ=2PE and FR=PF+3 , then the length of PR is

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

PQRS is cyclic quadrilateral. Extended PQ and SR intersect each other at A . Prove that AP.AQ=AR.AS .