In the adjoining figure, seg RS is the diameter of the circle with centre 'O'. Point T is in the exterior of the circle. Prove that `/_RTS` is an acute angle.

In the adjoining figure, seg EF is the diameter of the circle with centre H. Line DF is tangent at point F. If r is the radius of the circle, then prove that DE xxGE=4r^2 .

In the adjoining figure, seg AB is a diameter of a circle with centre O. the bisector of angleACB intersects the circle at point D. Prove that ,seg ADcongseg BD .

In the adjoining figure, seg AB is a diameter of a circle with centre C. Line PQ is a tangent, which touches the circle at point T. Seg AP bot line PQ and seg BQ bot line PQ. Prove that seg CP cong seg CQ.

In the adjoining figure, Point O is the centre of the circle. Length of chord AB is equal to the radius of the circle. Find /_ACB

In the adjoining figure, Point O is the centre of the circle. Length of chord AB is equal to the radius of the circle. Find m(arc AB)

In the adjoining figure, seg AB is a diameter of a circle with centre O. Bisector of inscribed /_ACB intersects circle at point D. prove: seg AD~=seg BD

In the adjoining figure, Point O is the centre of the circle. Length of chord AB is equal to the radius of the circle. Find m(arc ACB)

In the adjoining figure,O is the centre of the circle.Find the value of /_ABP if /_POB=90^@ .

In the adjoining figure,Point O is the centre of the circle.Length of chord AB is equal to the radius of the circle.Find (i) /_AOB

In the above figure, seg AB is a diameter of a circle with centre P.C is any point on the circle. Seg CE _|_ seg AB. Prove that CE is the geometric mean of AE and EB. Write the proof with the help of following steps: (a) Draw ray CE. It intersects the circle at D. (b) Show that CE = ED. Write the result using theorem of intersection of chords insides a circle. (d) Using CE = ED, complete the proof.