pm is a tangent to a circle with centre o touching the circle at m if op=85 cm and pm=77cm find the radius of circle
Answers
Step-by-step explanation:
Given
pm is a tangent to a circle with centre o touching the circle at m if op=85 cm and pm=77 cm find the radius of circle
We need to find the radius of the circle.
MOP is a triangle with M = 90 degree
We know that OP^2 = PM^2 + OM^2
85^2 = r^2 + 77^2
7225 = r^2 + 5929
So r^2 = 7225 – 5929
= 1296
So r = 36 cm
Therefore radius of the circle will be 36 cm
Answer:
36cm
Step-by-step explanation:
The radius is always perpendicular to the tangent at the point of tangency
In this circle the radius OM is perpendicular to the tangent PM since the radius OM touches the circle at the point of tangency M
The tangent and the radius forms and angle of 90° with the radius
Line PO forms a slanted height as it connects the tangent and the center of the circle
It is correct to say that the figure formed is a right angled triangle
Line PO is the hypotenuse and tangent PM is the base of the triangle
We can use the Pythagorean theorem to find the height OM which is the radius of the circle
H² = Hyp² - B²
H is the height , hyp is the hypotenuse and B is the base
H² = 85² - 77²
7225 - 5929 = 1296
H² = 1296
H = √1296
H = 36 cm
The radius of the circle is 36cm