Q. 14.2( 27 Votes )

AD is a diameter A. 17 cm

B. 15 cm

C. 4 cm

D. 8 cm

Answer :


Given: Diameter of the circle = d = AD = 34 cm


Radius of the circle = r = d/2 = AO = 17 cm


Length of chord AB = 30 cm


Since the line drawn through the center of a circle to bisect a chord is perpendicular to the chord, therefore AOL is a right angled triangle with L as the bisector of AB.


AL = 1/2(AB) = 15 cm


In right angled triangle AOB, by Pythagoras theorem, we have:


(AO)2 = (OL)2 + (AL)2


(17)2 = (OL)2 + (15)2


(OL)2 = (17)2 - (15)2


(OL)2 = 289 – 225


(OL)2 = 64


Take square root on both sides:


(OL) = 8


The distance of AB from the center of the circle is 8 cm.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Tips to Solve RD Sharma Problems FasterTips to Solve RD Sharma Problems FasterTips to Solve RD Sharma Problems Faster23 mins
Smart Revision | Most Important Questions of CirclesSmart Revision | Most Important Questions of CirclesSmart Revision | Most Important Questions of Circles45 mins
RD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma | Extra Qs. of Cyclic Quadrilaterals31 mins
NCERT | Imp Qs Discussion on CirclesNCERT | Imp Qs Discussion on CirclesNCERT | Imp Qs Discussion on Circles39 mins
Smart Revision | World of CirclesSmart Revision | World of CirclesSmart Revision | World of Circles44 mins
Smart Revision | Chords and Related ConceptsSmart Revision | Chords and Related ConceptsSmart Revision | Chords and Related Concepts42 mins
Let's Solve Good Questions on CircleLet's Solve Good Questions on CircleLet's Solve Good Questions on Circle41 mins
Some Imp Concepts Of CirclesSome Imp Concepts Of CirclesSome Imp Concepts Of Circles44 mins
NCERT | Quiz on CirclesNCERT | Quiz on CirclesNCERT | Quiz on Circles45 mins
Concept of Cyclic QuadrilateralConcept of Cyclic QuadrilateralConcept of Cyclic Quadrilateral61 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
RELATED QUESTIONS :

Prove that there RS Aggarwal & V Aggarwal - Mathematics

Number of circlesRD Sharma - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

The question consRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In the give figurRS Aggarwal & V Aggarwal - Mathematics

Prove that an angRS Aggarwal & V Aggarwal - Mathematics