Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • In fig 3 from an external point P two tangents PT and PS are drawn to a circle with centre O and raidus r

In fig 3 from an external point P , two tangents PT and PS are drawn to a circle with centre O and raidus r . 

If OP = 2r , show that \angle OTS = \angle OST = 30 \degree

 

 

 

 
 
 
 
 

Answers (1)

OP = 2r 

 OT = OS = r 

To prove 

\angle OTS = \angle OTS = 30 \degree

In \Delta OTP = 90 \degree \\\\ \sin ( \angle OPT ) = \frac{OT }{OP} = \frac{r}{2r} = 1/2 \\\\ \angle OTP = 30 \degree

\angle OTP + \angle OPT + \angle TOP = 180 \degree \\\\ 90 \degree + 30 \degree + \angle TOP = 180 \degree \\\\ \angle TOP = 60 \degree \\\\ or \angle TOQ = 60 \degree ---- (1)

Now in 

\Delta OTQ \: \:and \: \: \Delta OSQ \\\\ OT = OS (radius) \\\\ OQ = OQ (common ) \\\\ \angle OTQ = \angle OSQ

By SAS congruence 

\Delta OTQ \simeq \Delta OSQ \\\\ by \: \: CPCT \\\\ \angle TOQ = \angle SOQ \\\\ \angle TOQ = \angle SOQ = 60 \degree ----- (2) \\\\ now , \angle TOS = \angle TOQ + \angle SOQ \\\\ \angle TOS = \angle TOQ + \angle TOQ \\\\ \angle TOS = 2 \angle TOQ \\\\ \angle TOS= 2 \times 60 \degree

\angle TOS=120 \degree --- (3)\\\\ now \Delta TOS \\\\ OT = OS \\\\ \angle OTS = \angle OST \\\\ \angle TOS + \angle OTS + \angle OST = 180 \degree \\\\ \angle OTS + \angle OTS + 120 = 180 \degree \\\\ 2 \angle OTS = 60 \degree \\\\ \angle OTS = 30 \degree \\\\ \angle OTS = \angle OST = 30 \degree

Hence proved 

 

 

Posted by

Ravindra Pindel

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Result 2025: DigiLocker access code out; schools to download for Class 10, 12 students
anam-khan

CBSE Class 10, 12 result process revised; answer book photocopy now comes before re-evaluation
anam-khan

CBSE Class 10 result 2025 not expected this week, 'confirms' Board amid ruckus over result date

Latest Question