Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Circles" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. A point P is 10 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal toa)4 cmb)5 cmc)6 cmd)None of these.Correct answer is option 'C'. Can you explain this answer?

Question

Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter &#34;Circles&#34; are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. A point P is 10 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal toa)4 cmb)5 cmc)6 cmd)None of these.Correct answer is option 'C'. Can you explain this answer?

Answer

ΔPTO is a right angled triangle at T ,where the tangent touches the circle.
So applying pythagoras theorem,
H²=P²+B²
10²=B²+8²
B=

Radius is 6cm.

Answer

Applying pgt we get 100 -64= 36 and 36 is sq of 6
so the answer is option c i.e 6

Answer

Solution:

Given:
Point P is 10 cm from the centre of the circle.
Length of the tangent drawn from P to the circle is 8 cm.

To find:
The radius of the circle.

Let's assume:
The centre of the circle as O and the radius as r.

Now, we can form a right-angled triangle using the given information.
The line joining the centre O and the point of contact between the tangent and the circle forms the hypotenuse of the triangle.
The length of the tangent is the opposite side of the triangle and the distance from the centre to the tangent is the adjacent side of the triangle.

Using the Pythagorean Theorem, we can write:
(OP)^2 = (OT)^2 + (PT)^2
where OP is the hypotenuse, OT is the adjacent side, and PT is the opposite side.

Given that OP = 10 cm and PT = 8 cm, we can substitute these values into the equation:
(10)^2 = (OT)^2 + (8)^2
100 = (OT)^2 + 64
100 - 64 = (OT)^2
36 = (OT)^2

Taking the square root on both sides, we get:
OT = √36
OT = 6 cm

Therefore, the radius of the circle is 6 cm.
Hence, option C is the correct answer.

Answer

ΔPTO is a right angled triangle at T ,where the tangent touches the circle.
So applying pythagoras theorem,
H²=P²+B²
10²=B²+8²
B=

Radius is 6cm.

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