A geometry problem by dhruv kaushik

Geometry Level 2

In the given figure, AP and BP are tangents to the circle with centre O. If angle CBP = 25 degree and angle CAP = 40 degree, find angle APB........???

Give the answer in only numeric values. E.g.- If answer is 90 degree, write answer as 90. Do not write the answer like 90 degree or 90^o.

                                                                                                        BEST OF LUCK!!!


The answer is 50.

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1 solution

Prince Stalwart
Nov 8, 2014

GIVEN: AP and BP are tangents to the circle with centre O. Therefore, angle OAP=90 degree and angle OBP=90 degree. Now, it is given that: angle CBP=25 degree. Therefore, arc CB subtends an angle of (2X25=50 degree) at the centre O. Similarly, angle CAP=40 degree. Thus, arc CA subtends an angle of (2X40=80 degree) at the centre O. Therefore, the complete angle AOB=(50+80)=130 degree at centre O. Now, in Quadrilateral AOBP we have, angle AOB+ angle OAP+ angle OBP+ angle APB= 360 degree 130+ 90+ 90+ angle APB= 360 degree Thus, angle APB=(360-130-90-90) angle APB= 50 degree.

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