In the adjoining figure, chord AD and BC of a circle are produced to meet at P, PA = 10 cm, PB = 8 cm, PC = 5 cm, AC = 6 cm. Find BD, PD.

5.8, 3

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3.8, 5

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2.8, 6

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4.8, 4

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Solution

The correct option is D
4.8, 4

In Triangles ACP and BDP; $a = a_{1}$ ( $∠$ in same seg.); p=p (common)
$∠ A C P = ∠ B D P$ (3rd $∠$ of triangle)
$\Rightarrow$ Triangle ACP $\sim$ Triangle BDP(A.A.A.)
$\frac{B D}{B P} = \frac{A C}{A P}$ {corr. sides of similar triangles}
$\Rightarrow \frac{B D}{8} = \frac{6}{10} \Rightarrow B D = 4.8 c m \frac{P D}{B P} = \frac{P C}{A P}$ {Corr. sides} $\frac{P D}{8} = \frac{5}{10}$
$\Rightarrow P D = \frac{40}{10} = 4 c m$

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Similar questions

Q. In the figure, chords

B A

and

D C

of a circle meet at

P

. Prove that

P A \times P B = P C \times P D

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