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Quantitative Aptitude

Triangles

If C_1:x^2+y^...

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{ If }C_1:x^2+y^2=(3+2\sqrt2)^2 be a circle. }PA and }PB}{ are pair of tangents on }C_1 where }P is any point on the }}{ director circle of }C_1, then the radius of the smallest }}{ circle which touches }C_1 externally and also the two }}{ tangents }PA and }PB is

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C_{1} : x^{2} + y^{2} = (3 + 2 \sqrt{2})^{2}

be a circle and PA and PB are pair of tangents on

C_{1}

, where P is any point on the director circle of

C_{1}

, then the radius of smallest circle which touch

C_{1}

externally and also the two tangents

P A

P B

S : x^{2} + y^{2} = 9

P A

P B

are pair of tangents on

S

P

is any point on the director circle of

S

, then the radius of the smallest circle which touches

S

externally and also the two tangents

P A

P B

α + β \sqrt{2}

. Then the value of

α + β

C_{1}

C_{2}

are two concentric circles, the radius of

C_{2}

being twice that of

C_{1}

P

C_{2}

P A

P B

C_{1}

. Prove that the centroid of the triangle

P A B

C_{1}

Q. Tangents are drawn from a point

P

C : x^{2} + y^{2} = a^{2}

C_{1} : x^{2} + y^{2} = b^{2}

. These tangents cut the circle

C

Q

R

Q R

C_{1}

, then the area of

△ P Q R

C_{1}

C_{2}

are two concentric circles having centre at the origin with radii

2 and 4,

respectively. If

P A

P B

are two tangents to

C_{1}

P

C_{2}

, then the locus of centroid of

Δ P A B

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