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Circles

In  Figure,  common tangents AB and CD to two circles  intersect  at  E. Prove that AB = CD.

Circles

In Figure, AB and CD are common  tangents  to  two circles  of  unequal  radii. Prove that AB = CD.

Circles

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Circles

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.

Circles

 Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

Circles

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.

Circles

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.

Circles

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.

Circles

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.

Circles

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.