Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Prove that the lengths of two tangents drawn from an external point to a circle are equal.         <div style="float:l

Prove that the lengths of two tangents drawn from an external point to a circle are equal.

 

 

 

 
 
 
 
 

Answers (1)

Let circle with centre O has two tangents AB and AC.

To prove \rightarrow AB=AC

Construction \rightarrow Join AO, BO and OC

Proof \rightarrow  OB \perp AB\; \; \text{and}\; \; OC\perp AC  (Tangent at any point of the circle is perpendicular to the radius)

\Rightarrow \angle OBA= \angle OCA=90^{\circ}

In \bigtriangleup ABO and  \bigtriangleup ACO

\Rightarrow \angle OBA= \angle OCA  (both 90^{\circ})

\Rightarrow OB=OC                 (radius of the circle)

\Rightarrow OA=OA                 (common)

By R.H.S congruency  \bigtriangleup ABO \cong \bigtriangleup ACO

Hence by CPCT : AB=AC

Hence proved.

 

 

Posted by

Ravindra Pindel

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE mandatory 3rd language rule leaves Sanskrit as only R3 option at many pvt English-medium schools
anam-khan

CBSE directs schools to roll out three-language policy’s R3 structure for Class 6 within 7 days
anam-khan

CBSE Result 2026 Date and Time LIVE: Phase 1 Class 10 results expected soon at results.cbse.nic.in

Latest Question