Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?a)11cmb)13 cmc)10 cmd)12cmCorrect answer is option 'C'. Can you explain this answer?

Question

Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?&#8203;a)11cmb)13 cmc)10 cmd)12cmCorrect answer is option 'C'. Can you explain this answer?

Answer

Length of tangent = 24 cmLength from the point to the centre of circle = 26 cm.
Join the point of contact and the centre of the circle.
We know that line drawn from centre to the tangent is always perpendicular.
So by using Pythagoras Theorem,
(26)^2 = (24)^2 + Square of other side.
(Other side)^2 = 676 - 576.
Other side = √100.
Other side = 10 cm

Answer

Answer

Given:
Distance of point from the center of the circle = 26 cm
Length of the tangent from the point to the circle = 24 cm
To find: Radius of the circle

Solution:
Let O be the center of the circle and P be the point from where the tangent is drawn.

From the given information, we can draw a right-angled triangle OPR (where R is the point of intersection of the tangent and circle) as shown below:

![image.png](attachment:image.png)

We know the following:
OP = 26 cm (distance of point from the center)
PR = 24 cm (length of tangent)
OR = radius of the circle (to be found)

Using Pythagoras theorem in triangle OPR, we get:
OR^2 = OP^2 - PR^2
OR^2 = 26^2 - 24^2
OR^2 = 676
OR = √676
OR = 26 cm

Therefore, the radius of the circle is 10 cm (Option C).

Answer: Option C (10 cm)

Answer

You are provided with the perpendicular(distance from center) and hypotenous(length of tangent)............using pythagoreon's theoram find base i.e, radius of circle
h^2-p^2=b^2
(26)^2 - (24)^2=(100)^1/2 =10

Answer

As tangent to a circle make a right angle so by Pythagores theorem . we can prove it.
as tangent =24 CM
distance from Center to the point = 26
we had to find radii=?
by applying Pythagoras Theorem
26 sq= 24 sq +radii sq
radii sq = 676-576
radii= under root 100
radii= 10

may this help u

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