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Standard X

Mathematics

Apollonius's Theorem

In Δ ABC, ...

Question

In $Δ A B C$ , $D$ is a point on side $B C$ . If $A C = 3$ cm, $A D = 3$ cm, $B D = 8$ cm and $C D = 1$ and then $A B$ is:

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Solution

From $Δ A B P, x^{2} - {8.5}^{2} = A P^{2}$
From $Δ A D P, 9 - \frac{1}{4} = A P^{2}$
$\Rightarrow x^{2} - {8.5}^{2} = 9 - \frac{1}{4} = \frac{35}{4}$
$\Rightarrow x^{2} = \frac{289 + 35}{4} = \frac{324}{4} = 81$
$\Rightarrow x = 9$ m

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In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
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(iii) If Ab = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

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(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

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In ΔABC, D is a point on side BC. If AC=3 cm, AD=3 cm, BD=8 cm and CD=1 and then AB is:

From ΔABP,x2−8.52=AP2From ΔADP,9−14=AP2⇒x2−8.52=9−14=354⇒x2=289+354=3244=81⇒x=9 m

In $Δ A B C$ , $D$ is a point on side $B C$ . If $A C = 3$ cm, $A D = 3$ cm, $B D = 8$ cm and $C D = 1$ and then $A B$ is:

From $Δ A B P, x^{2} - {8.5}^{2} = A P^{2}$
From $Δ A D P, 9 - \frac{1}{4} = A P^{2}$
$\Rightarrow x^{2} - {8.5}^{2} = 9 - \frac{1}{4} = \frac{35}{4}$
$\Rightarrow x^{2} = \frac{289 + 35}{4} = \frac{324}{4} = 81$
$\Rightarrow x = 9$ m