Find the value of angle in degree made by the tangent of a circle with the radius of that circle at the point of contact

From an external point P of a circle with centre O, two tangents PS and PT are drawn. QS is a chord of the circle parallel to PT. If ∠SPT = 80°, then find the value of ∠QST.

Find the number of direct common tangents of two circles which touch each other externally.

If two circles touch each other internally, then the number of common tangents of the circles are (a) 1 (b) 2 (c) 3 (d) 4

State True or False: Two concentric circles have only one common tangent.

If two circles do not intersect or touch each other, then the maximum number of common tangents is/are: (a) 2 (b) 1 (c) 3 (d) 4

If two tangents are drawn to a circle from a point outside it, then prove that the line segments joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.

Two circles touch each other externally at point C. A direct common tangent AB touches the two circles at points A and B. Find the value of ∠ACB.

A circle with the center 'O'. A point P is 26 cm away from the center of the circle, and the length of the tangent drawn from the point P to the circle is 10 cm. Calculate the length of the radius of the circle.

ABCD is a circumscribed quadrilateral of a circle with centre O. Show that AB + CD = AD + BC

Prove that the tangent to a circle at any point on it is perpendicular to the radius that passes through the point of contact.

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”