AB is the diameter of the circle with centre O. P is a point on the circle such

Sail E0 Webinar

Question

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d, then BP = _____.

Options:

A .

\sqrt{2} d

B .

\frac{d}{\sqrt{5}}

C .

\sqrt{5} d

D .

2 \sqrt{2} d

Answer: Option B
:
B

Let O be the centre of the circle. The angle subtended by an arc at the center is twice the angle subtended by it at any point on the remaining part of the circle. (here that point is P).
$∠ A O B = 180^{\circ}$
$\Rightarrow ∠ A P B = \frac{∠ A O B}{2} = 90^{\circ}$

$∴ △ A P B$ is a triangle, right angled at $P$ .
$\Rightarrow$ By pythagoras theorem,
${A B}^{2} = {A P}^{2} + {P B}^{2} = {(2 P B)}^{2} + {P B}^{2} = 5 {P B}^{2}$
$\Rightarrow A B = \sqrt{5} P B$

$\Rightarrow P B = \frac{A B}{\sqrt{5}} = \frac{d}{\sqrt{5}}$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller triangle is 2.1 cm, then t....then the corresponding height of the bigger triangle is _____.

Question 2. All congruent figures are similar but the similar figures need not be congruent. ....

Question 3. In the figure below, if the line segment ST is parallel to line segment QR such that PSSQ=PTTR. The provided data is no....sufficient to prove that triangles PQR and PST are similar.

Question 4. In both the figures given below, all of the respective sides are equal and all interior angles are 90∘. Are the figur....interior angles are 90∘. Are the figures shown below similar?

Question 5. In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 find the area of �....and area of triangle ABC=54cm2 find the area of △ DEF__ cm2

Question 6. If the sides of two similar triangles are in the ratio of 4 : 9, then the areas of these triangles are in the ratio __....the areas of these triangles are in the ratio ____.

Question 7. A farmer had three land plots as shown. He has to divide the plots equally among 2 of his sons. He gives Area a and Area....True if he has given equal area else enter false.

Question 8. In ΔABC, AB=BC=6cm. If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then ....intersects AB and BC at E and D, then ΔABC∼ΔEBD.

Question 9. In the given figure, ∠ABC = 90∘ and BM is a median, AB = 8 cm and BC = 6 cm. Then, choose the correct option(s).....and BC = 6 cm. Then, choose the correct option(s).

Question 10. In the given figure, △ABC∼△PQR. Then, area of △ ABCarea of △ PQR equals ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0