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:

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

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

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

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:

Angle subtended by a chord AB on the centre of the circle is 140 degree. What will be the angle subtended by the chord AB on the major are of the circle? 

In a triangle, if three altitudes are equal, then the triangle 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