In Fig. 10.69, AB is a diameter of a circle with centre O and AT is a tangent. If , find .(CBSE 2015)

In Fig. 2, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent P and Q. (CBSE 2013)

In fig XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that, XA+AR+AB+BR. (CBSE 2014)

In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with center O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°. (CBSE 2016)

in fig. 4, O is the center of a circle such that diameter AB = 13 am and AC = 12 cm. BC is joined. Find the area of the shaded region. (Taken π = 3.14) (CBSE 2016)