## Plane Geometry

#### Plane Geometry

1. ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then ∠BCD is :

1. As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

Given , ∠COD = 120°
∠BAC = 30°

 ∠CAD = 1 × ∠COD 2

 ∠CAD = 1 × 120° = 60° 2

##### Correct Option: B

As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

Given , ∠COD = 120°
∠BAC = 30°

 ∠CAD = 1 × ∠COD 2

 ∠CAD = 1 × 120° = 60° 2

∴ ∠BCD = 180° - ∠BAD
∴ ∠BCD = 180° – 90° = 90°

1. The radius of two concentric circles are 9 cm and 15 cm. If the chord of the greater circle be a tangent to the smaller circle, then the length of that chord is

1. According to question , we draw a figure of a circle with centre O ,

Here , BO = OC = 15 cm and OD = 9 cm.
From ∆ BDO ,
∴ BD = √BO² - OD²

##### Correct Option: A

According to question , we draw a figure of a circle with centre O ,

Here , BO = OC = 15 cm and OD = 9 cm.
From ∆ BDO ,
∴ BD = √BO² - OD²
∴ BD = √15² - 9²
BD = √24 × 6 = 12 cm
∴ BC = 2 × 12 = 24 cm.

1. ABC is an isosceles triangle such that AB = AC and ∠B = 35°. AD is the median to the base BC. Then ∠BAD is:

1. Firstly , We draw a figure of an isosceles triangle ABC ,

Given that , AB = AC and ∠B = 35°
⇒ ∠ABC = ∠ACB = 35°

##### Correct Option: D

Firstly , We draw a figure of an isosceles triangle ABC ,

Given that , AB = AC and ∠B = 35°
⇒ ∠ABC = ∠ACB = 35°
⇒ ∠ BAD + 90° + 35° = 180°

1. The centroid of a triangle is the point where

1. As we know the point of intersection of medians of a triangle is called centroid.

##### Correct Option: A

As we know the centroid of a triangle is the point where the point of intersection of medians of a triangle is called centroid.

1. AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is

1. According to question ,
D, is the mid-point of side BC. Point O is the centroid that divides AD in the ratio 2 : 1.
we draw a figure triangle ABC whose point O is centroid ,

##### Correct Option: B

According to question ,
D, is the mid-point of side BC. Point O is the centroid that divides AD in the ratio 2 : 1.
we draw a figure triangle ABC whose point O is centroid ,

AO = 10 cm
∴ OD = 5 cm.