AB is an tangent to a circle with center P touching the circle at B. PA intersects the circle at M. If AB =35cm and AM=25cm find diameter of the circle.
Answers
If tangent to the circle AB =35 cm and PA intersects the circle at M where AM=25 cm, then the diameter of the circle is 24 cm.
Step-by-step explanation:
Let the radius of the circle be “r” cm such that PM = PB = r cm …. (i)
We know that a tangent to a circle is perpendicular to the radius through the point of contact, therefore,
angle PBA = 90°
Also given, AB = 35 cm and AM = 25 cm
Now referring to the figure attached below, by using Pythagoras theorem, in ∆ APB, we get
AP² = AB² + BP²
⇒ [25 + r]² = 35² + x² ….. [substituting values from (i) and other given values]
⇒ 625 + 50x + r² = 1225 + r²
⇒ 50r = 1225 – 625
⇒ r = 600/50
⇒ r = 12 cm
Thus,
The diameter of the circle is given as,
= 2*r
= 2 * 12 …… [substituting r = 12 cm]
= 24 cm
++++++++++++++++++++++++++++++++++++++++++++++++++
Also view:
What is circle tangent and secant give proper definition
https://brainly.in/question/8461924
Prove that tangent is perpendicular to radius
https://brainly.in/question/1015009
Answer:
24cm
Step-by-step explanation:
hope it help you...........