Visualisation of Pythagoras' Theorem

Q.

The points $(a,a),(–a,-a)$ and $(–\sqrt{3}a,\sqrt{3}a)$ are the vertices of a/an _____ triangle.

1. scalene

2. right angled

3. isosceles right angled

4. equilateral

Q.

Two pillars of height 8 m and 14 m are 8m apart, find the distance between their top.

1. 20 m

2. 10 m

3. 15 m

4. 9 m

Q.

Rohit walks 80 m towards left and then turns right. How much distance should he walk now so that the minimum distance between the initial and final point is 100 m? ___

Q.

In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.

1. $x=-3,y=-7$

2. $x=3,y=7$

3. $x=9,y=14$

4. $x=3,y=14$

Q.

Alpha drives 8 km to the north and 15 km to the east. Find the distance between the starting point and the terminating point

1. 16 km

2. 17 km

3. 27 km

4. 23 km

Q. The houses of 4 friends are located at the points (6, 6), (0, 6), (3, 3) and (6, 0) as shown in the figure. A, C and B are the vertices of a right triangle. Find the distance between the houses at points B and D.

1. 3$\sqrt{2}\text{units}$
2. 2$\sqrt{5}\text{units}$
3. 2$\sqrt{3}\text{units}$
4. $\sqrt{6}\text{units}$

Q.

Question 11 (ii)
State whether the following are true or false. Justify your answer.
(ii) sec A = $\frac{12}{5}$ for some value of angle A.

Q.

The tangent to a circle from a point outside the circle measures 15cm. The distance of the point from the centre is 12cm. The radius of the circle is

1. 10cm

2. 11cm

3. 8cm

4. 12cm

Q. Two pillars of length 8 m and 14 m stand up vertically with the ground. If the distance between the bases is 8 m, then find the distance between the top ends of the pillars.

1. 20 m
2. 10 m
3. 15 m
4. 9 m

Q. The area of an isosceles triangle is $60c{m}^2$ and the length of each one of its equal sides is 13 cm. Find its base.
[4 MARKS]

Q. The value of AD in the given figure is

1. 17 m
2. 13 m
3. 18 m
4. 19 m

Q. Question 5
Two circles with centers O and O’ of radii 3 cm and 4 cm , respectively intersect at two points P and Q, such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.

Q.

Shyam is on top of a building of 80m height waving at his friend Ram who is 60m away from the building. what is the direct distance between Ram and Shyam?

1. 50m

2. 70m

3. 100m

4. 130m

Q. Question 4
Area of the largest triangle that can be inscribed in a semi – circle of radius r units is:
(A) $r^{2}squnits$
(B) $\frac{1}{2}{r}^{2}squnits$
(C) $2r^{2}squnits$
(D) $\sqrt{2}{r}^{2}squnits$

Q. In an isosceles $\Delta ABC$ right angled at B, prove that $A{C}^2=2A{B}^2.$

Q.

A 13 m ladder is leaned against a wall as shown in figure. Find the distance of foot of ladder from the wall.

1. 1 m

2. 25 m

3. 2 m

4. 5 m

Q. If the radius of a circle is 5 cm & length of a tangent PA from an external point P is 12 cm.Find the distance of point P from the centre of circle.

Q.

Vikram travels 4 m east, take a right turn and again travels for 3 m. How far is he from the starting point?

1. 3 m

2. 5 m

3. 1 m

4. 7 m

Q. Which of the following are true for the parallelogram given below with dimensions 17 cm$\times$ 15 cm?

1. $h=\sqrt{116}$ m
2. $h=\sqrt{187}$ m
3. Area = 255 $m^2$
4. Area = 183$m^2$

Q. Refer to the following figure. Three squares are constructed on each side of a right angled triangle as shown, with the side of each square equal to the length of the side on which it is constructed. If the largest side measures 13 units, then the sum of the areas of the three squares is :

1. 576 sq. units
2. 169 sq. units
3. 338 sq. units
4. 625 sq. units

Q.

The top of a broken tree touches the ground at a distance of $12\mathrm{m}$ from its base. If the tree is broken at a height of $5\mathrm{m}$ from the ground then the actual height of the tree is

1. $25\mathrm{m}$

2. $13\mathrm{m}$

3. $18\mathrm{m}$

4. $17\mathrm{m}$

Q.

A square is inserted inside a circle such that the corners of the square coincide with the circumference of the circle. If the diameter of the circle is d, the area of the shaded part is ____$c{m}^2$.

___

Q.

The area of a circle which encloses a square of side 10 cm is :

1. $25\pi$

2. $50\pi$

3. $75\pi$

4. $100\pi$

Q. If the hypotenuse of a right angled triangle is $h$ and perpendicular sides are $a$ and $b$, then

1. $h=a+b$
2. $h^2=a^2+b^2$
3. $h^2+b^2=3a^2$
4. $h^3=3(a^3+b^3)$

Q. Write ‘True’ or ‘False’ and justify your answer in each of the following :
(i) The length of tangents from an external point P on a circle is always greater than the radius of the circle.
(ii) The length of tangents from an external point P on a circle with centre O is always less than OP.

Q.

Shyam is on top of a building of 80m height waving at his friend Ram who is 60m away from the building. what is the direct distance between Ram and Shyam?

1. 50m

2. 100m

3. 130m

4. 70m

Q. A rectangle $ABCD$ is inscribed in a circle with a diameter lying along the line $3y=x+10$. If $A$ and $B$ are the points $(-6,7)$ and $(4,7)$ respectively then

1. centre of the circle is $(-1,3)$
2. centre of the circle $(-1,0)$
3. area of the rectangle is $100sq.units$
4. area of the rectangle is $80sq.units$

Q.

A square is inserted inside a circle such that the corners of the square coincide with the circumference of the circle. If the diameter of the circle is d�, the area of the shaded part is ____$c{m}^2$.

___

Q.

Vikram travels 4 m east, takes a right turn and again travels for 3 m. How far is he from the starting point?

1. 7 m

2. 3 m

3. 5 m

4. 1 m

Q. In the given figure, O is the centre of two concentric circles fo radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm. Find the length of BP.