Question

Let W X and Y Z be two diametrically opposite tangents of a circle with
center at O and touching points are P and Q respectively. Let another point on the line W X be S such that, P S : OP =√3 : 1. Now, let another tangent from S is drawn
and that tangent intersects Y Z at T. Find the ratio ST : OP.

Answer 1

Step-by-step explanation:

Answer:

Equation of given line is x+y=5

Slope of given line = −1

As this line is tangential to given circle at (2,3), so a line perpendicular to given line passing through (2,3) will also pass through center of given circle.

As product of slope of two mutually perpendicular lines =−1

So, slope of line perpendicular to given line =1

Equation of a line having slope =1 and passing through (2,3) is x−y=−1

This line passes through (1,2) and also the circle passes through (1,2)

So (1,2) and (2,3) are two diametrically opposite points on the circle.

Hence, radius = 2(2−1)2+(3−2)2

⇒ radius = 21

Step-by-step explanation:

$\huge{\tt{hi}}$

Answer 2

As this line is tangential to given circle at (2,3), so a line perpendicular to given line passing through (2,3) will also pass through center of given circle.

As product of slope of two mutually perpendicular lines =−1

So, slope of line perpendicular to given line =1

Equation of a line having slope =1 and passing through (2,3) is x−y=−1

This line passes through (1,2) and also the circle passes through (1,2)

So (1,2) and (2,3) are two diametrically opposite points on the circle.

Hence, radius = 2(2−1)2+(3−2)2

⇒ radius = 21