In the 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 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 _|_ line PQ and seg BQ _|_ line PQ. Prove that, seg CP ~= seg CQ.

In figure, seg RS is a diameter of the circle with centre O. Point T lines in the exterior of the circle. Prove that /_RTS is an acute angle.

In the adjoining figure, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that angleRTS is an acute angle.

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 . Complete the following proof by filling the blanks.

In the figure , seg AB is the chord of the circle with centre O. if AM =4 cm then find MB and AB. State your reason.

In figure, seg AB is a diameter of a circle with centre O. The bisector of /_ACB intersects the circle at point D. Prove that seg AD cong seg BD. Complete the following proof by filling in the blanks

In the figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion.

Seg AB is a diameter of a circle with centre P. Seg AC is a chord. A secant through P and parallel to seg AC intersects the tangent drawn at C in D. Prove that line DB is a tangent to the circle.

In the adjoining figure, O is the centre and seg AB is a diameter. At the point C on the circle, the tangent CD is drawn. Line BD is a tangent to the circle at the point B. Show that segOD || chord AC.

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 folloing 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.