two circles with centres a and b have radii 5 cm and 3 cm,touch each other internally if - Maths -

Question

two circles with centres a and b have radii 5 cm and 3 cm,touch
each other internally if the perpendicular bisector of the segment
ab meet the bigger circle at p and q find length of pq

Aakash Sharma · Accepted Answer

Given : Two circles with centers a and b have radii 5 cm and 3 cm,touch each other internally â‡’ ab = radius of bigger circle - radius of smaller circle = 5 cm - 3 cm = 2 cm Now, the perpendicular bisector of the segment ab meet the bigger circle at p and q Let this perpendicular bisector intersect ab at o â‡’ $a o = \frac{a b}{2} = \frac{2}{2} = 1 c m$ So, In right Î”aop ap2 = ao2 + op2 â‡’ op2 = ap2 + ao2 = (5 cm)2 - (1 cm)2 = (25 - 1)cm2 = 24 cm2 â‡’ op = $\sqrt{24} = 2 \sqrt{6}$ cm Similarly, In right Î”aoq oq = $2 \sqrt{6}$ cm Hence, pq = op + oq = $2 \sqrt{6} + 2 \sqrt{6} = 4 \sqrt{6}$ cm

two circles with centres a and b have radii 5 cm and 3 cm,touch each other internally . if the perpendicular bisector of the segment ab meet the bigger circle at p and q .find length of pq