PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and  APB = 600 , then find the length of the chord AB.

Slide27.JPG

Slide28.JPG
Slide29.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and  APB = 600 , then find the length of the chord AB. We know that Tangent from external point are equal ∴ PA = PB Since angles opposite equal sides are equal Thus, ∠ PAB = ∠ PBA By Angle Sum property in Δ APB ∠ APB + ∠ PAB + ∠ PBA = 180° 60° + ∠ PAB + ∠ PAB = 180° 60° + 2∠ PAB = 180° 2∠ PAB = 180° − 60° 2∠ PAB = 120° ∠ PAB = (120° )/2 ∠ PAB = 60° Thus, in Δ APB ∠ PAB = ∠ PBA = 60° And, ∠ APB = 60° Since all angles are 60°, ∴ Δ APB is an equilateral triangle 60° + ∠ PAB + ∠ PAB = 180° 60° + 2∠ PAB = 180° 2∠ PAB = 180° − 60° 2∠ PAB = 120° ∠ PAB = (120° )/2 ∠ PAB = 60° Thus, in Δ APB ∠ PAB = ∠ PBA = 60° And, ∠ APB = 60° Since all angles are 60°, ∴ Δ APB is an equilateral triangle Since in equilateral triangle All sides are equal ∴ AB = AP = 6 cm

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.