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Question

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If POR=72o, PTR is
239880_67ab0c6eb7e64cb38e4deace944efc20.png

A
118o
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B
36o
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C
54o
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D
26o
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Solution

The correct option is B 54o
GivenPQisadiameterofacirclewithcentreO.PTisatangenttothecirclefromTatP.QTintersectsthecircleatR.POR=72o.TofindoutPTR=?SolutionThediameterPQortheradiusOPmeetsthetangentPTatP.PQPTsincetheradiusthroughthepointofcontactofatangenttoacircleisperpendiculartothetangent.QPT=90o.AgaintheminorarcPRsubtendsPORtothecentreOandPQRtothecicumference.PQR=12×POR=12×72o=36o.SoinΔPQTQTP=180o(PQR+QPT)(byanglesumpropertyoftriangles)=180o(36o+90o)=54o.AnsOptionC.

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