Question : A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:
Option 1: $2 \sqrt{3} {~cm}$
Option 2: $\sqrt{19} {~cm}$
Option 3: $\sqrt{17} {~cm}$
Option 4: $3 \sqrt{2} {~cm}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\sqrt{19} {~cm}$
Solution : Given: OP = 17 cm, PA=12 cm and PB = 22.5 cm We know, Two chords AB and CD when extended meet at point P, then PA × PB = PC × PD Let the radius be x. ⇒ PC = 17 – x and PD = 17 + x According to Question- PA × PB = PC × PD ⇒ 12 × 22.5 = (17 – x)(17 + x) ⇒ 270 = 289 – x$^2$ ⇒ x$^2$ = 19 ⇒ x = $\sqrt{19}$ cm Hence, the correct answer is $\sqrt{19}$ cm.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : Let O be the centre of the circle and P be a point outside the circle. If PAB is a secant of the circle which cuts the circle at A and B and PT is the tangent drawn from P, then find the length of PT, if PA = 3 cm and AB = 9 cm.
Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
Question : Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.
Question : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O
Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile