A geometry problem by aman vats
Geometry
Level
pending
FIND ANGLE (AGB)
GIVEN THAT I is the incenter of the triangle ABC. P and Q are tangent points.
The answer is 90.
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1 solution
Join IQ . Angle IQP will be equal to angle C/2.(alternate angle theorem) Angle IGP will be equal to -90+b/2+c/2 As we know that angle IAP will be a/2 Then angle IGP +angle IAP=90+a/2+b/2+c/2=90+90=180 This shows that quadrilateral AIGP will be a cyclic . As we know that angle API will be 90 (line joining centre and tangent) Hence, Angle AGB will also be equal to angle API (angles in same segment) Therefore, Angle AGB =90