Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If ∠CAB = 34°, then measure of ∠CBA is

If the orthocenter and the centroid of a triangle are the same, then the triangle is:

If ABC is an equilateral triangle and D is a point on BC such that AD⊥BC, then 

Point P lies outside a circle with centre O. Tangents PA and PB are drawn to meet the circle at A and respectively. If ∠APB =80⁰, then ∠OAB is is equal to:

If C₁, C₂ be the centres of rwo circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is