Q. 4 A5.0( 1 Vote )

Solve any two sub

Answer :

Consider the following figure


A circle with center O and radius r and A be the external point from which tangents AX and AY are drawn


A line drawn from center to the point of contact of tangent and circle is perpendicular to tangent


Therefore OX is perpendicular to AX and OY is perpendicular to AY


To prove: AX = AY


OX and OY are radius of circle


OX = OY = r


Consider ∆AXO


AXO = 90°


by Pythagoras


AX2 + XO2 = AO2


AX2 = AO2 - XO2


AX2 = AO2 - r2



Consider ∆AYO


AYO = 90°


by Pythagoras


AY2 + YO2 = AO2


AY2 = AO2 - YO2


AY2 = AO2 - r2



From (i) and (ii) we conclude that


AX = AY


Hence proved


Therefore, the lengths of the two tangent segments to a circle drawn from an external point are equal.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Solve any two subMaharashtra Board - Geometry Papers

In figure 3.80, iMHB - Mathematics Part-2

In figure 3.79, OMHB - Mathematics Part-2

Two circles of raMHB - Mathematics Part-2

If radii of two cMHB - Mathematics Part-2

In figure 3.81, sMHB - Mathematics Part-2

Four alternative MHB - Mathematics Part-2

In fig 3.27, the MHB - Mathematics Part-2

In fig 3.28 the cMHB - Mathematics Part-2

Two circles havinMHB - Mathematics Part-2