The angles of a triangle are 40°, 60°, 80° and a circle touches its sides at P, Q, R, calculate the angles of triangle PQR?

I don't understand what the diagram will look like

1 Answer
CW
Apr 29, 2018

See explanation.

Explanation:

enter image source here
recall that tangent segments to a circle from an external point are equal in length,
#=> AP=AR, BP=BQ, and CQ=CR#,
#=> DeltaAPR, DeltaBPQ and DeltaCQR# are isosceles triangles.
#=> angleAPR=angleARP=(180-40)/2=70^@#
similarly, #angleBPQ=angleBQP=(180-60)/2=60^@#
similarly, #angleCQR=angleCRQ=(180-80)/2=50^@#
#=> angleRPQ=180-70-60=50^@#
#anglePQR=180-60-50=70^@#
#anglePRQ=180-70-50=60^@#

Footnote : #DeltaBPQ# is actually an equilateral triangle.

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