Q. 64.2( 6 Votes )

If angle between

Answer :

False

Let us consider a circle with center O and tangents PT and PR and angle between them is 60° and radius of circle is a .



In OTP and ORP


TO = OR [ radii of same circle]


OP = OP [ common ]


TP = PR [ tangents through an external point to a circle are equal]


OTP ORP [ By Side Side Side Criterion ]


TPO = OPR [Corresponding parts of congruent triangles are equal ] [1]


Now, TPR = 60° [Given]


TPO + OPR = 60°


TPO + TPO = 60° [By 1]


TP0 = 30°


Now, OT TP [ As tangent at any point on the circle is perpendicular to the radius through point of contact]


OTP = 90°


So POT is a right-angled triangle


And we know that,



So,


[As OT is radius and equal to a]




So the above statement is false .


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