Mathematics - Circle Question with Solution | TestHub

MathematicsCircleGeneral, Basic geometries, Definition Diametrical form of circleHard2 minQB

MathematicsHardmultiple choice

If $Q, S$ are two points on the circle $x^{2} + y^{2} = 4$ such that the tangents $QP, SR$ are parallel. If $PS, QR$ intersect at T then $(\frac{QT}{PQ})^{2} + (\frac{ST}{RS})^{2} + PQ \cdot RS \neq =$

Options:(select one or more)

Answer:

A, B, C

Solution:

$QTS = ∠ PTQ = \frac{π}{2}$ as QS is diameter

$\frac{QT}{PQ} = sin θ, \frac{ST}{RS} = cos θ, \frac{4}{PQ} = tan θ, \frac{4}{RS} = cot θ$ $∴ (\frac{QT}{PQ})^{2} + (\frac{ST}{RS})^{2} + PQ \cdot RS = sin^{2} θ + cos^{2} θ + (4 cot θ) (4 tan θ)$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:General, Basic geometries, Definition Diametrical form of circle

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...