two cords AB and CD intersect at P inside a circle.Proove thatthe sum of the angles subtended by the arcs AC and BD at the centre O is equal to twice the angle APC. 

Asked by Hemant Arora | 13th Oct, 2014, 01:01: PM

Expert Answer:

L e t space angle B O D equals space 2 x comma space angle A O C equals 2 y comma space angle D C B equals x comma space angle A B C equals y I n space triangle P B C comma angle P B C plus angle P C B equals x plus y equals e x t. space angle B P D A l s o space angle B P D equals angle A P C therefore angle A P C equals x plus y angle B O D plus space angle A O C equals 2 x plus 2 y equals 2 left parenthesis x plus y right parenthesis equals 2 left parenthesis angle A P C right parenthesis H e n c e space P r o v e d

Answered by Prasenjit Paul | 14th Oct, 2014, 10:00: AM

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