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CBSE Class 10 Answered

Explain angle on same segment. ( i.e., angle subtended on the chord is equal to angle formed by the chord and tangent )
 
Prove it . 
Asked by sucharitasahoo1 | 14 Oct, 2017, 08:50: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style GIven colon space straight A space circle space with space centre space straight O. space Tangent space PQ thin space touches space the space circle space at space point space straight A. space Through space straight A comma space the space point space of space contact comma space straight a space chord space AB space is space drawn. To space prove colon space angle BAQ equals angle ACB space space and space space angle BAP equals angle ADB Proof colon In space triangle ABR comma angle ABR equals 90 degree space space space space space left parenthesis Angle space of space straight a space semi minus circle right parenthesis rightwards double arrow angle ARB plus angle RAB equals 90 degree space space space space space space space.... left parenthesis straight i right parenthesis angle OAQ equals 90 degree space space space space space space space space space space left parenthesis Angle space between space the space radius space and space the space tangent right parenthesis rightwards double arrow angle RAB plus angle BAQ equals 90 degree space space space space space space.... left parenthesis ii right parenthesis rightwards double arrow angle ARB plus angle RAB equals angle RAB plus angle BAQ space space space space space space space.... left square bracket From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis right square bracket rightwards double arrow angle ARB equals angle BAQ space space space But comma space angle angle ARB equals angle ACB space space space space space space left parenthesis Angles space of space the space same space segment right parenthesis space space rightwards double arrow angle BAQ equals angle ACB space space space space space space left parenthesis proved right parenthesis Now comma space angle BAP plus angle BAQ equals 180 degree and space angle ACB plus angle ADB equals 180 degree space space space space space left parenthesis opposite space angles space of space cyclic space quadrilateral right parenthesis rightwards double arrow angle BAP plus angle BAQ equals angle ACB plus angle ADB rightwards double arrow angle BAP equals angle ADB space space end style
Answered by Rashmi Khot | 04 Dec, 2017, 03:17: PM

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