(1)Given AB is the tangent to the circle with centre C.

CAB = 90˚ [The tangent at any point of a circle is perpendicular to the radius through the point of contact.]

(2) Line AB seg CA. [Tangent theorem]

CA is the radius of the circle.

CA = 6cm

Distance of point C from AB is 6cm.

(3)In CAB , A = 90˚.

AC = 6 [radius]

AB = 6

BC^{2} = AC^{2}+AB^{2} [Pythagoras theorem]

BC^{2} = 6^{2}+6^{2}

BC^{2} = 72

Taking square root on both sides

BC = √72 = 6√2 cm

d(B,C) = 6√2 cm.

(4)InABC , AB = AC = 6

ABC is an isosceles triangle.

Angles opposite two equal sides will be equal in isosceles triangle.

C = B……..(i)

A = 90˚ [Tangent theorem]

A + C +B = 180 [Angle sum property of triangle]

90+ C +B = 180

C +B = 90

C = B = 45˚ [From (i)]

ABC = 45˚