Question

6. In each of the following figures, O is the centre of the circle. Find the values of z and
y.
Tangent
12 cm
15 cm
8 cm
y cm Tangent
x cm
T2
Р
x cm
x cm
15cm o
y cm
24 cm
y cm
Tangent
Р
18 cm
Tangent T
(111)
(ii)
Objective Type Questions
MENTAL MATHS
1. Fill in the blanks:
its end points​

Answer 1

Answer:

6. In each of the following figures, O is the centre of the circle. Find the values of z and

y.

Tangent

12 cm

15 cm

8 cm

y cm Tangent

x cm

T2

Р

x cm

x cm

15cm o

y cm

24 cm

y cm

Tangent

Р

18 cm

Tangent T

(111)

(ii)

Objective Type Questions

MENTAL MATHS

1. Fill in the blanks:

its end points

Answer 2

Step-by-step explanation:

Solutions:-

1)Given figure is a semi-circle.

We know that

The angle in a semi circle is 90°

So the triangle in the semi circle is a right angled triangle

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

=> x² = 15²+8²

=> x² = 225+64

=> x² = 289

=> x² = 17²

=>x = 17 cm

given that

x = 2y

=> y = x/2

=>y = 17/2

=> y = 8.5 cm

2) P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

=> x² = 12²+5²

=> x² = 144+25

=> x² = 169

=> x² = 13²

=> x = 13 cm

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

y = 12 cm

3)P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

=> OP² = OT1² +PT1²

=> x² = 24²+18²

=> x² = 576+324

=> x² = 900

=>x² = 30²

=> x = 30cm

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

PT1 = PT2

y = 18 cm

Answer:-

1) x = 17 cm and y = 8.5 cm

2) x = 13 cm and y = 12 cm

3) x = 30 cm and y = 18 cm

Used formulae:-

• The angle between the radius of the circle and the tangent at the point of contact is 90°
• The square of the hypotenuse is equal to the sum of the squares of the other two sides.
• The angle in a semi circle is 90°