In the fig. `angleQPR=anglePQR` and L and M are respectively on sides QR and PR of PQR such that QL=PM prove that OP=OQ, where O is the point of intersection of PL and QM

PQR is a triangle right angled at P and M is a point on QR such that PM _|_ QR . Show that PM^2 = QM.MR .

PQR is a triangle right angled at P and M is a point on QR such that PM bot QR. Show that PM^2 = QM.MR.

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

In fig., A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR. .

In fig. ABCD is a quadrilateral and L and M are respectively points on AD and CD such that AB=BC, angleABL=angleCBM and angleLBD=angleMBD . Prove that BL=BM.

In Fig, 6.21 , A, B and C are points on OP, OQ and OR respectively such that AB||PQ and AC||PR. Show that BC||QR.

The vectors from the origin O to the points P and Q are respectively 2 hat i-6 hat j+3 hat k and -2 hat i+hat j+2 hat k . Determine the area of the parallelogram formed by vec OP and vec OQ as adjacent sides.

Diagonals PR and QS of a quadrilateral PQRS intersect each other at O. Prove that PR + QR + RS + SP

Diagonals PR and QS of a quadrilateral PQRS intersect each other at O. Prove that PR + QR + RS + SP

In the fig. l||m and O is the mid point of the line segment. Prove that O is also the mid point of any line segment CD having its end points on l and m respectively