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GradeTangent to a Circle

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The tangent to the circle \[x^{2} + y^{2} = 9\] which is parallel to the y axis and does not lie in the third quadrant touches the circle at the point

A. \[( - 3,\ 0)\]

B. \[(3,\ 0)\]

C. \[(0,\ 3)\]

D. \[(0,\ - 3)\]

A. \[( - 3,\ 0)\]

B. \[(3,\ 0)\]

C. \[(0,\ 3)\]

D. \[(0,\ - 3)\]

Let S be the circle in the X-Y plane defined by the equation \[{{x}^{2}}+{{y}^{2}}=4\]. let P be a point on the circle S with both coordinates being positive. let the tangents to S at P Intersect the coordinate axes at the points M and N. then the midpoint of the segment MN must lie on the curve.

A. \[{{(x+y)}^{2}}=3xy\]

B. \[{{x}^{\dfrac{2}{3}}}+{{y}^{\dfrac{2}{3}}}={{2}^{\dfrac{4}{3}}}\]

C. \[{{x}^{2}}+{{y}^{2}}=2xy\]

D. \[{{x}^{2}}+{{y}^{2}}={{x}^{2}}{{y}^{2}}\]

A. \[{{(x+y)}^{2}}=3xy\]

B. \[{{x}^{\dfrac{2}{3}}}+{{y}^{\dfrac{2}{3}}}={{2}^{\dfrac{4}{3}}}\]

C. \[{{x}^{2}}+{{y}^{2}}=2xy\]

D. \[{{x}^{2}}+{{y}^{2}}={{x}^{2}}{{y}^{2}}\]

In the given figure, PQ is a tangent from an external point P to a circle with center O, and OP cuts the circle at T and QOR is a diameter. If $\angle POR={{130}^{\circ }}$ and S is a point on the circle, find $\angle 1+\angle 2$

A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

A. m(m + n)

B. m + n

C. n(m + n)

D. \[\dfrac{1}{2}\left( {m + n} \right)\]

A. m(m + n)

B. m + n

C. n(m + n)

D. \[\dfrac{1}{2}\left( {m + n} \right)\]

The straight line $x+2y=1$ meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B from tangent to the circle at origin is:

A. $\dfrac{\sqrt{5}}{4}$

B. $\dfrac{\sqrt{5}}{2}$

C. $2\sqrt{5}$

D. $4\sqrt{5}$

A. $\dfrac{\sqrt{5}}{4}$

B. $\dfrac{\sqrt{5}}{2}$

C. $2\sqrt{5}$

D. $4\sqrt{5}$

In figure if TP and TQ are the two tangents to a circle with center O so that $\angle POQ = {110^0},$ the $\angle PTQ$ is equal to.

A.${60^0}$

B.${70^0}$

C.${80^0}$

D.${90^0}$

A.${60^0}$

B.${70^0}$

C.${80^0}$

D.${90^0}$

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect a point x on the circumference of the circle, then 2r equals-

A) $\sqrt {PQ.RS} $

B) $\dfrac{{PQ + RS}}{2}$

C) $\dfrac{{2PQ + RS}}{{PQ + RS}}$

D) $\sqrt {\dfrac{{P{Q^2} + R{S^2}}}{2}} $

A) $\sqrt {PQ.RS} $

B) $\dfrac{{PQ + RS}}{2}$

C) $\dfrac{{2PQ + RS}}{{PQ + RS}}$

D) $\sqrt {\dfrac{{P{Q^2} + R{S^2}}}{2}} $

Find the diameter of the sun in Km supposing that it subtends an angle of 32â€™ at the eye of the observer. Given that the distance of the sun from the observer $=91\times {{10}^{6}}km$

Find the length of the tangent from the point $$\left( {5,7} \right)$$ to the line $${x^2} + {y^2} - 4x - 6y + 9 = 0$$?

Two circles with equal radii are intersecting at the points (0, 1) and (0, -1). The tangent at the point (0, 1) to one of the circles. Then the distance between the centres of these circles is:

A. 1

B.\[\sqrt{2}\]

C. 2$\sqrt{2}$

D. 2

A. 1

B.\[\sqrt{2}\]

C. 2$\sqrt{2}$

D. 2

What are the tools required for constructing a tangent to a circle?

A.Ruler

B.Compass

C.Pencil

D.All the above

A.Ruler

B.Compass

C.Pencil

D.All the above

In the figure XY and Xâ€™Yâ€™ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and Xâ€™Yâ€™ at B prove that $\angle {\text{AOB = 9}}{{\text{0}}^\circ}$.

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