Suppose A B , A C and B C have lengths 13 , 14 and 15 respectively. If A F F B = 2 5 and C E E A = 5 8 . Find B D and D C .

Given that A B = 13 , A C = 14 and B C = 15 . Let B D = x and D C = y Using Ceva's theorem, we have, B D D C × C E E A × A F F B = 1 ... 1 Substitute the values of A F F B and C E E A in 1 , We have B D D C × 5 8 × 2 5 = 1 ⇒ x y × 10 40 = 1 ⇒ x y × 1 4 = 1 ⇒ x = 4 y ... 2 So, B C = B D + D C = 15 x + y = 15 ... 3 Substitute the value of x in equation 3 4 y + y = 15 5 y = 15 y = 3 Substitute y = 3 in equation 2 x = 4 × 3 = 12 Hence, B D = 12 c m and D C = 3 c m

E M B I B E

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 30

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10th Tamil Nadu Board

IMPORTANT

Earn 100

Draw a circle of radius $4 cm$ . At a point $L$ on it draw a tangent to the circle using the alternate segment.

Important Questions on Geometry

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 31

Draw a circle of diameter

6 cm

. From a point

P

, which is

8 cm

away from its centre, draw the two tangents

PA

and

PB

to the circle and measure their lengths.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 32

Show that in a triangle, the medians are concurrent.

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 33

In the given figure, $A B C$ is a triangle with $∠ B = 90^{o}$ , $B C = 3 cm$ and $A B = 4 cm$ . $D$ is point on $A C$ such that $A D = 1 cm$ and $E$ is the midpoint of $A B$ . Join $D$ and $E$ and extend $D E$ to meet $C B$ at $F$ . Find $B F$ .

Question Image

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 34

Suppose

A B, A C

and

B C

have lengths

13, 14

and

15

respectively. If

\frac{A F}{F B} = \frac{2}{5}

and

\frac{C E}{E A} = \frac{5}{8}

. Find

B D

and

D C

.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Standard 10>Chapter 4 - Geometry>Solved Example>Q 35

In a garden containing several trees, three particular trees $P, Q, R$ are located in the following way, $B P = 2 m, C Q = 3 m, R A = 10 m, P C = 6 m, Q A = 5 m, R B = 2 m$ where $A, B, C$ are points such that $P$ lies on $B C, Q$ lies on $A C$ and $R$ lies on $A B$ . Check whether the trees $P, Q, R$ lie on a same straight line.