Calculate `T_(P)` and `T_(Q)` (P is mid point)

A B C is a triangle right angled at B ; a n d\ P is the mid-point of A C . Prove that: P Q\ _|_A B (ii) Q is the mid point of A B P B=P A=1/2A C

In Fig. 10.62, P O_|_Q O . The tangents to the circle at P and Q intersect at a point T . Prove that P Q and O T are right bisectors of each other. (FIGURE)

Let P\ a n d\ Q be any two points. Find the coordinates of the point R\ which divides P Q externally in the ratio 2:1 and verify that Q is the mid point of P R .

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

P Q is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T . Find the length T P .

In Fig. , the side QR of △ PQR is produced to a point S. If the bisectors of /_P Q R and /_P R S meet at point T, then prove that /_Q T R=1/2/_Q P R .

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A C . If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C .

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

In Figure, P Q R S is a quadrilateral and T\ a n d\ U are respectively points on P S and R S such that P Q=R Q ,\ /_P Q T=/_R Q U\ a n d\ /_T Q S=/_U Q Sdot Prove that Q T=Q Udot

In Figure, T is a point on side Q R of P Q R and S is a point such that R T=S Tdot Prove That : P Q+P R > Q S