Question

In the given figure, OCB is a semicircle with OB as diameter. If OC = 3 units, which of
following is correct?
(a) a2+ b2 = 9
(b) a2 + (b – 5)2 = 16
(c) a2 + b2 = 16
(d) a2 + b2 – 10a + 9 = 0

Answer 1

Step-by-step explanation:

Given: In figure OCB is a semicircle with OB as diameter. If OC = 3 units.

To find: Which of the following is correct?

(a) a²+ b² = 9

(b) a² + (b – 5)²= 16

(c) a² + b² = 16

(d) a² + b² – 10a + 9 = 0

Solution:

Tip: Chords from end points of diameter meet at 90°.

Distance formula:(x1,y1) and (x2,y2)

$\bf \sqrt{ {(x_2 - x_1)}^{2} + ( {y_2 - y_1)}^{2} }$

Thus, OCB is a right triangle, right angle at C.

OB= Diameter = 5 units

In Right triangle we can apply Pythagoras theorem.

Hypotenuse² = Base²+ Perpendicular²

$OB²=OC²+BC²$

Length of OC =3 units

Length of BC: Distance between C(a,b) and B(5,0)

Length of BC

$= \sqrt{( {5 - a)}^{2} + ( {0 - b)}^{2} }$

simplify

$BC= \sqrt{25 + {a}^{2} - 10a + {b}^{2} }$

Apply Pythagoras theorem

$( {5)}^{2} = ( {3)}^{2} + ( { \sqrt{ {a}^{2} - 10a + 25 + {b}^{2} } })^{2}$

or

$25 = 9 + {a}^{2} - 10a + 25 + {b}^{2}$

simplify

${a}^{2} + {b}^{2} - 10a + 9 = 0$

Final answer:

Option d is correct.

$\bf \red{{a}^{2} + {b}^{2} - 10a + 9 = 0}$

Hope it helps you.

To learn more on brainly:

if ∆ABC ~∆EDF such that Ab=5cm ,ac 10 cm ,ed =12cm and DF 24cm then eg snd bc are respectively equal to

https://brainly.in/question/47874179

Answer 2

Answer:

here ans can be both a and  d

Step-by-step explanation:

follow it..-

triangle angle subtended in a semi circle is 90 deg

ob =5 (by fig)

oc=3 given

by pytho

bc=4 cm

so here it also follows a^2 +b^2=9

ans A and d