MATHSIn the figure, the radius of the SMALLER circle is 3 centimetres, that of the bigger circle is 6 centimetres and the DISTANCE between the centres of the circles is 15 centimetres. PQ is a tangent to both the circles. Find its length.627950MEDIUMShareStudy laterVIDEO EXPLANATIONANSWERLet O be the centre of the smaller circle and R be the centre of the bigger circle.Join OP, RQ and OR. Let M be the point of intersection of PQ and OR. In △POM and QRM∠OPM=90 o =∠RQM[∵ Tangent to the circle is perpendicular to the radius drawn at the point of contact with the circle.]∠OMP=∠RMQ [OPPOSITE angels]∴△POM∼QRM by AA test of similarity.∴ RQOP = RMOM = QMPM RQOP = RMOM ⇒ 63 = RMOM ⇒RM=2OM ...........(1)RQOP = QMPM ⇒ 63 = QMPM ⇒QM=2PM .............(2)In △POM using Pythagoras Theorem,OM 2 =OP 2 +PM 2 5 2 =3 2 +PM 2 PM=4cmQM=2PM [from (2)]PQ=PM+MQ=4+8=12cm∴ The length of tangent PQ is 12cm.solutionAnswered Bytoppr71 ViewsHow satisfied are you with the answer?This will help us to improve betteranswrGet Instant Solutions, 24x7No Signup requiredgirlMore Questions by difficultyEASYMEDIUMHARDstarPractice important QuestionsKerala Board 2015 Class 10 Maths26 QsRelated Questions to studylx+my+n=0 is a tangent line to the circle x 2 +y 2 =r 2 , if-MEDIUMStudy laterView ANSWERIN figure, OP is equal to diameter of the circle. Prove that ABP is an equilateral triangle.1251737MEDIUMStudy laterView AnswerVIEW MORERevise with ConceptsProblems on Circles and LinesEXAMPLEDEFINITIONSFORMULAESstarBROWSE BYClassesBoardsExamsMODULESOnline ClassesMock TestsAdaptive PracticeLive DoubtsStay upto date with our Newsletter!Stay informed, stay ahead. Be a topperYour email addressAbout UsBrand ResourcesPressCustomer StoriesJobsEducatorsFellowshipLearning PlanetGuidesAskBlogBytesNewsTerms of ServicePrivacy PolicyContact UsFAQsGoogle PlayApp StoreINIndia