From a point P outside a circle with centre at C, tangents PA and PB are drawn such that `(1)/((CA)^(2)) +(1)/((PA)^(2))=(1)/(16)`, then the length of chord AB is

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that (i) /_AOP=/_BOP (ii) OP is the _|_ bisector of chord AB.

From a point P, two tangents PA and PB are drawn such that PA=10 cm and angleAPB=60^(@). Find the length of chord AB.

If tangents PA and PB are drawn from P(-1, 2) to y^(2) = 4x then

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the product of the slopes of these tangents is 1, then the locus of P is a conic whose eccentricity is equal to

Tangents PA and PB are drawn to x^(2) + y^(2) = 4 from the point P(3, 0) . Area of triangle PAB is equal to:-

In Figure, there are two concentric circles with centre O of radii 5 cm and 3 cm . From an external point P , tangents PA and PB are drawn to these circles. If A P=12 cm , find the length of BPdot

C1 and C2 are two concentric circles, the radius of C2 being twice that of C1. From a point P on C2, tangents PA and PB are drawn to C1. Then the centroid of the triangle PAB (a) lies on C1 (b) lies outside C1 (c) lies inside C1 (d) may lie inside or outside C1 but never on C1

From the point P(3, 4) pair of tangents PA and PB are drawn to the ellipse (x^(2))/(16)+(y^(2))/(9)=1 . If AB intersects y - axis at C and x - axis at D, then OC. OD is equal to (where O is the origin)

From the point P(3, 4) tangents PA and PB are drawn to the circle x^(2)+y^(2)+4x+6y-12=0 . The area of Delta PAB in square units, is

In the given figure, PA and PB are tangents to a circle from an external point P such that PA=4 cm and angleBAC=135^(@). Find the length of dhord AB.