0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

# Two tangents are drawn from a point P to the circle x2+y2−2x−4y+4=0, such that the angle between these tangents is tan−1(125), where tan−1(125)∈(0,π). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of ΔPAB and ΔCAB is:

A
11:4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
9:4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
2:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 9:4Given : x2+y2−2x−4y+4=0 r=√1+4−4=1tanθ=125 Respective areas are ΔPAB=12×L2sinθΔCAB=12×r2sin(π−θ)⇒ΔPABΔCAB=(Lr)2⇒ΔPABΔCAB=cot2θ2⇒ΔPABΔCAB=2cos2θ22sin2θ2⇒ΔPABΔCAB=1+cosθ1−cosθ⇒ΔPABΔCAB=1+5131−513=94

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Extrema
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program