
PQ is a tangent to a circle with centre O at the point P. If is an isosceles triangle with P as a vertex , then is equal to
a)
b)
c)
d)
Answer
406.8k+ views
Hint: We are given that PQ is a tangent to a circle with centre O at the point P. Let us consider OP to be the radius of the circle. Then, as PQ is tangent at point P, we know the tangent makes a right angle with the radius. Hence, . Also, we are given that is an isosceles triangle. We will understand this using a diagram.
In the given figure, OP is the radius of the circle and PQ is tangent at point P. Hence, . Since is an isosceles triangle, we have two sides of this triangle are equal. Let us consider . Now, we will use the property of an isosceles triangle that angles opposite to equal sides are equal. After that we will use the angle sum property of a triangle i.e. Sum of angles in a triangle is equal to and find the required angle.
Complete step-by-step solution:
Since PQ is a tangent at point P and OP is the radius of the circle.
We see it through a figure.
We know, tangent makes a right angle with the radius and So,
As is an isosceles triangle with .
We know, Angles opposite to equal sides are equal.
Angle opposite to is .
Angle opposite to is .
Hence,
In , using Angle Sum Property
Using (1) and (2) in (3)
Subtracting both the sides, we get
Clubbing the like terms on left hand side
Solving the left and the right hand side
Dividing both the sides by .
Hence, we got .
Therefore, the correct option is (b).
Note: We need to be very thorough with the properties of circles and triangles. Once we interpret the given question, we need to think of the steps of solving the problem. While solving, we need to take care of the calculations. We have to read the question carefully and then draw the figure and then apply the properties. Each and every detail in the question needs to be read very carefully. While solving, we have to take care of each and every step.

In the given figure, OP is the radius of the circle and PQ is tangent at point P. Hence,
Complete step-by-step solution:
Since PQ is a tangent at point P and OP is the radius of the circle.
We see it through a figure.

We know, tangent makes a right angle with the radius and So,
As
We know, Angles opposite to equal sides are equal.
Angle opposite to
Angle opposite to
Hence,
In
Using (1) and (2) in (3)
Subtracting
Clubbing the like terms on left hand side
Solving the left and the right hand side
Dividing both the sides by
Hence, we got
Therefore, the correct option is (b).
Note: We need to be very thorough with the properties of circles and triangles. Once we interpret the given question, we need to think of the steps of solving the problem. While solving, we need to take care of the calculations. We have to read the question carefully and then draw the figure and then apply the properties. Each and every detail in the question needs to be read very carefully. While solving, we have to take care of each and every step.
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
Where did Netaji set up the INA headquarters A Yangon class 10 social studies CBSE

A boat goes 24 km upstream and 28 km downstream in class 10 maths CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

The British separated Burma Myanmar from India in 1935 class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What are the public facilities provided by the government? Also explain each facility
