Question

In the figure, two circles with centres A and B and radii 5 cm and 3 cm touching each other internally. If the perpendicular bisector of segment AB, meets the bigger circle at P and Q, find the length of PQ.

Answer 1

$\huge{\mathfrak{\underline{\underline{Solution}}}}$

Given:

A and B are the centres of the circles with radii 5cm and 3cm respectively.

C is the mid-point of AB.

Extend AB upto O point on circumference of outer circle.

AB=AO−BO=5−3=2cm (since AO and BO are radii of larger and smaller circles)

AB = $\sf{\frac{A}{B}}$ = $\sf{\frac{2}{2}}$ = 1cm

Now in right angled triangle AMP

AC =1cm, AP=5cm

By pythagoras theorem,

AP² = PC² + AC²

PC² = √AP² - AC²

PC² = √5² - 1²

Therefore, PQ = 2PC = 2√24 = 4√6cm

[CP = CQ]

So, PQ = 4√6cm

_____________________________

Hope it helps uh<33