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

In what ratio is the segment joining (-1,-12) and (3,4) divided by the x-axis?

Chord AB of circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P, then the length of the tangent AP (in cm) 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:

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

In △ABC, D and E are points on sides AB and AC, such that DE||BC. If AD=x+3, DB=2x-3, AE=x+1 and EC=2x-2, then the value of x is