Question
Download Solution PDFIn the following figure, O is the centre of the circle. If OP = 5 cm and radius of the circle is 3 cm, find the length of the tangent PT.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
O is the center of the circle.
OP = 5 cm
Radius of the circle (OT) = 3 cm
PT is a tangent to the circle at point T.
Formula Used:
The radius to the point of tangency is perpendicular to the tangent. Therefore, ∠OTP = 90°.
Pythagorean theorem: In a right-angled triangle, (hypotenuse)2 = (base)2 + (perpendicular)2
In right-angled triangle OTP, OP is the hypotenuse, OT and PT are the other two sides.
Calculation:
In right-angled triangle OTP, by the Pythagorean theorem:
OP2 = OT2 + PT2
52 = 32 + PT2
25 = 9 + PT2
PT2 = 25 - 9
PT2 = 16
PT = \(\sqrt{16}\) = ±4
Since length cannot be negative, PT = 4 cm.
The length of the tangent PT is 4 cm.
Last updated on Dec 9, 2024
-> SSC Head Constable (AWO/TPO) 2025 Notification will be announced soon.
-> SSC Head Constable (AWO/TPO) Marks were out for the previous cycle. Candidates could check their marks from the official website till 15th February 2024.
-> The total number of vacancies for the SSC Head Constable 2025 Notification will be declared soon. The candidates earlier appeared for the exam for a total number of 857 vacancies for SSC Head Constable Recruitment for the 2022 cycle.
->The candidates who will be qualified in the CBE gets eligible for the Physical test. Candidates can improve their preparations and score high by referring to SSC Head Constable AWO TPO Previous Years Papers and SSC Head Constable (AWO/TPO) Mock Test.