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CBSE Class 10 Answered

Tangents drawn from an external point P touches circle with centre O and radius 5 cm at T. If OP Intersects circle at B and PT=12 Find BT
Asked by mpps199821 | 20 Feb, 2020, 11:48: PM
answered-by-expert Expert Answer
 
Triangle OTP is right-angled triangle at T
Using Pythagoram thm, we have
OP squared equals OT squared plus PT squared equals 25 plus 144 equals 169 rightwards double arrow OP equals 13 space cm Since comma space OB space equals space 5 space cm rightwards double arrow PB space equals space 8 space cm Now comma space in space triangle OTP comma cos angle POT equals OT over OP equals 5 over 13 rightwards double arrow cos angle BOT equals 5 over 13 BT squared equals OB squared plus OT squared minus 2 space cross times space OB cross times OT space cos angle BOT equals 25 plus 25 minus 2 space cross times space 5 space cross times space 5 space cross times 5 over 13 equals 50 open parentheses 1 minus 5 over 13 close parentheses equals 50 cross times 8 over 13 equals 400 over 13 rightwards double arrow BT equals fraction numerator 20 over denominator square root of 13 end fraction
Answered by Renu Varma | 24 Feb, 2020, 11:46: AM

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