Write ‘True’ or ‘False’ and justify your answer.
AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = BD.
Write ‘True’ or ‘False’ and justify your answer.
If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.
Write ‘True’ or ‘False’ and justify your answer.
If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ.
Write ‘True’ or ‘False’ and justify your answer.
The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.
Write ‘True’ or ‘False’ and justify your answer.
The angle between two tangents to a circle may be 0°.
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point P on a circle with centre O is always less than OP.
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
Write ‘True’ or ‘False’ and justify your answer.
If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.
In figure, PQL and PRM are tangents to the circle with centre O at the points Q and R, respectively and S is a point on the circle such that ∠SQL = 50° and ∠SRM = 60°. Then ∠QSR is equal to 40°.