Question

PQ is a chord of length 16cm, of a circle of radius 10cm. the tangents at P and Q intrest at a point T. find the length of TP.

Answer 1

Answer: answer of above question is following

Step-by-step explanation:

Answer 2

Answer:

$Length \:of \:the \\tangent (PT)= \frac{40}{3}\: cm$

Step-by-step explanation:

Given chord length (PQ) = 16cm,

Radius (OP) = 10cm

Tangent (PT) = ?

i) PR = RQ = PQ/2 = 8cm

/* The perpendicular from the centre of a circle to a chord bisects the chord */

ii) In right triangle ORP,

<ORP = 90°,

By Phythagorean theorem:

OR² = OP² - PR²

= 10² - 8²

= 100 - 64

= 36

=> OR = 6 cm,

iii ) Let TR = x , PT = y

In ∆OPR and ∆OPT,

<POR = <POT

<PRO = <OPT = 90°

∆OPR ~ ∆OPT (AA similarity)

$\frac{PT}{PR} =\frac{OP}{OR}$

$\implies \frac{y}{8}=\frac{10}{6}$

$\implies y = \frac{10\times 8}{6}\\=\frac{40}{3}\:cm$

Therefore,

$Length \:of \:the \\tangent (PT)= \frac{40}{3}\: cm$

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