from a point p,40cm away from the centre ,a tangent pt of length 32cn is drawn. then find the radius of the circle
Answers
Answer:
radius of circle =24 cm
tangent form a right angled triangle from its centre
so,PTO is alright angled triangle where <pto=90 degree
isliye by Pythagoras Theory
PO^2 = PT^2 + OT^2
40^2 = 32^2 + OT^2
1600 = 1024 + OT^2
1600 - 1024 = OT^2
576 = OT^2
OT = √576
OT = 24
Radius of circle = 24 cm
Step-by-step explanation:
from a point p,40cm away from the centre
Let say center of circle = o
=> op = 40 cm
tangent pt of length 32cm
=> pt = 32 cm
Radius of circle = ot
ot² = op² - pt² ( applying pythagoras theorem)
=> ot² = 40² - 32²
applying a² - b² = (a + b)(a - b)
=> ot² = (40 + 32)(40 - 32)
=> ot² = 72 * 8
=> ot² = 9 * 8 * 8
=> ot² = 3² * 8²
=> ot = 3 * 8
=> ot = 24
Radius of circle = 24 cm
Learn more:
Two circles with radii 25 cm and 9 cm touch eachother externally ...
https://brainly.in/question/14673322
the length of tangent to a circle which is 13cm distance from the ...
https://brainly.in/question/14791961