If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.
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.
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