Q. 125.0( 1 Vote )

In the given figure, AB and AC are tangents to a circle with center 0 and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is


A. 9

B. 15

C. 353

D. 25

Answer :

As AB is tangent to the circle at point B


OB AB


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


In right angled triangle AOB,


By Pythagoras Theorem,


[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2 ]


(OA)2 = (OB)2 + (AB)2


(17)2 = (8)2 + (AB)2


[As OA = 17 cm is given and OB is radius]


289 = 64 + (AB)2


(AB)2 = 225


AB = 15 cm


Now, AB = AC [Tangents drawn from an external point are equal]


AC = 15 cm

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to CirclesQuiz | Areas Related to CirclesQuiz | Areas Related to Circles43 mins
RD Sharma |  Area of Sector and SegmentsRD Sharma |  Area of Sector and SegmentsRD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with CirclesQuiz | Area Related with CirclesQuiz | Area Related with Circles47 mins
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