Q1 of 35 Page 11

From a point P, the length of the tangent to a circle is 15 cm, and the distance of P from the centre of the circle is 17cm. Then what is the radius of the circle?

Let the centre of circle be O so that PO = 17 cm


Tangent is PB whose length is 15 cm


OB is radius as shown



Now we know that radius is perpendicular to point of contact


Hence OB is perpendicular to PB


Hence ∠PBO = 90°


Consider ΔPBO


Using Pythagoras theorem


⇒ PB2 + OB2 = PO2


⇒ 152 + OB2 = 172


⇒ OB2 = 172 - 152


⇒ OB2 = 289 – 225


⇒ OB2 = 64


⇒ OB = ±8


As length cannot be negative


⇒ OB = 8 cm


Hence length of radius is 8 cm


More from this chapter

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14

(i) From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at the point E and PA = 14 cm, find the perimeter of PCD.

(ii) If PA = 11cm, PD = 7 cm, then DE = ?


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In two concentric circles, prove that all chords of the outer circle which touch the inner arc of equal length.

 2

What is the distance between two parallel tangents of a circle of radius 10cm?

 3

If the distance between two parallel tangents of a circle is 10cm, what is the radius of the circle?