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ICSE Class 10 Answered

in the given figure, AP is a tangent to the circle at P. ABC is a secant such that PD PD IS THE BISECTOR OF angle BPC.
prove that angle BPD = 1/2 (angle ABP - angle APB)
 
 
Asked by Parvez | 26 Feb, 2016, 11:06: PM
answered-by-expert Expert Answer
AP space is space tangent space to space the space circle space and space ABC space is space secant. therefore AP squared equals AB cross times AC rightwards double arrow AB over AP equals AP over AC Also space angle PAB space equals space angle PAC therefore increment PAB tilde triangle PAC space space left parenthesis SAS space criterian right parenthesis therefore angle ABP space equals space angle APC equals angle APB space plus angle BPD space plus space angle DPC equals angle APB space plus 2 angle BPD angle ABP space minus space space angle APB space equals space 2 angle BPD angle BPD space equals space 1 half open parentheses angle ABP space minus space space angle APB space close parentheses
Answered by Vijaykumar Wani | 29 Feb, 2016, 12:10: PM

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